1

Angular Kinetics of Human Movement

1 Angular analogues of

ndash mass

ndash momentum

ndash impulse

ndash reaction force

2 Angular versions of Newtonrsquos Laws

of Motion

Resistance to Acceleration

How do we quantify resistance to linear acceleration

Mass

How do we quantify resistance to angular

acceleration

Moment of Inertia (I)

What directly influences I

I = mk2 so mass and the distribution of mass relative to axis of rotation affect I

Determining Moment of Inertia (I)I equals the sum of the products of (1) mass element of an object and (2) square of the distance between the mass element and axis of rotation

IAXIS = ΣΣΣΣmiri2

IAXIS = m1r12 + m2r2

2 + m3r32 + + mnrn

2

axis

r1

r2

m2m1

Determining Moment of InertiaA more practical approach

IAXIS = (mBODY)(k2)

k indicates the radius of gyration which is an experimentally determined length that applies to the whole object at once

k depends on the location of the axis and location of the mass

Whole-body IDifferent body segments have corresponding moments of inertia for each plane of motion

Similarly the whole human body rotating free of external force also has a moment of inertia relative to each of the cardinal axes

A BC

Whole-body IDifferent body segments have corresponding moments of inertia for each plane of motion

Similarly the whole human body rotating free of external force also has a moment of inertia relative to each of the cardinal axes

Inside Collection Textbook by Erik Christensen httpcnxorgcontentm42182latestcollection=col11435latest

2

ApplicationsWhy would someone choke up on a bat use an aluminum bat or illegally cork a wooden bat Is there a legal alternative

Applications

Applications

Tuck vs Layout for a diver or gymnast

A runners leg during swing phase

tucklayout

hip

Angular analogues for Newtonrsquos Laws of Motion

Newtonrsquos First Law

A rotating body will maintain a state of constant rotational motion unless acted on by an external torque

This is the basis for the principle of conservation of angular momentum (H)

What is Angular Momentum (H)

Momentum

bull For linear motion L = mv

bull For angular motion H = I ωωωω

Or H = (mk2) ωωωω

bull Factors that affect angular momentum (H)

ndash mass of the object (m)

ndash location of mass relative to axis or rotation (k)

ndash angular velocity of the object (ωωωω)

Units for angular momentum kgsdotsdotsdotsdotm2

s

Conservation of Angular Momentum (H)

Similar to L H for any given system remains constant in the absence of a net external

torque

However unlike the linear circumstances we discussed I and ω can change

So we cannot assume that either I or ω are conserved

throughout flight

3

Conserving Angular MomentumExample Problem A 60-kg diver is in a layout position (k = 05 m) immediately after leaving the board with an angular velocity of 4 rads What is the diverrsquos angular velocity when he assumes a

tuck position and reduces his radius of gyration to 025 m

k = 05 m

k = 025 m

Conservation of Angular Momentum

First find H when diver leaves the board

H = mk2ωωωω

H = (60 kg)(05 m)2(4 rads) = 60 kgsdotsdotsdotsdotm2s

H is constant so now find ωωωω when k is reduced to 025 m

60 kgsdotsdotsdotsdotm2s = (60 kg)(025 m)2 ωωωω

ωωωω = 16 rads

Falling cats

H about the long axis of the cat is initially zero and must be conserved throughout flight however the cat always rights itself How

Video Link

Although total body angular momentum is

conserved while the body is airborne (no external torques)

angular momentum can be transferred between body segments

Transfer of Angular Momentum

Also although total body angular momentum is conserved while the body is airborne (no

external torques) one can also change the total body axis of rotation (eg

a forward roll can become a twist)

Transfer of Angular MomentumFinally although angular momentum can be

transferred between body segments or the whole-body axis of rotation may changehellip

the whole-body center of mass must still follow a

parabolic trajectory while the body is airborne

4

Newtonrsquos Second Law

Torque causes angular acceleration as well as ∆H for a body that is directly proportional to

the magnitude of torque in the same direction as the torque and inversely proportional to

the bodyrsquos moment of inertia

ΣT = I αααα (compare with ΣF = m a)

Newtonrsquos Laws of Motion Angular Analogues

Net joint torque and knee pain

A Practice Problem The Answer

Angular Impulse amp Momentum

How does a person change H

external torque

Force torque and linear and angular impulse

ndash Linear Impulse = force timestimestimestimes time = F ∆∆∆∆ t

ndash Angular Impulse = torque timestimestimestimes time = T ∆∆∆∆ t

Impulse-momentum relationship

ndash Linear F ∆∆∆∆ t = ∆∆∆∆M F t = (mv)2 ndash (mv)1

ndash Angular T ∆∆∆∆ t = ∆∆∆∆H T t = (I ωωωω)2 ndash (I ωωωω)1

Practice ProblemsTo initiate a twisting jump Miki applies a force to the ice that results in a torque about her long axis Consequently H (about her long axis) increases from 0 to 50 kgmiddotm2s in 025 s During this time I (about her long axis) is 22 kgmiddotm2

1How large was the associated angular impulse (AI) Answer 50 Nmmiddots

2How large was the associated torque Answer 200 Nm

3How fast is Mikirsquos angular velocity (about her long axis) at the end of the 025 s Answer 227 rads or 316 revs

Miki Ando is one of a few female skaters to have landed a quadruple

jump (a salchow) in competition She first completed the jump at the 2002

ISU Junior Grand Prix Final in the Netherlands at age 15

5

Practice ProblemsIn order to rotate four times in the air during a single jump Miki must increase ω about her long axis

1 How can Miki manipulate I (about her long axis)

2 Is it beneficial for Miki to manipulate I (about her long axis) If so why

3 What might the overall effect of an increased or decreased I (about her long axis) be on her final score

Japanese figure skater Miki Ando is the only female skater to have landed a

quadruple jump (a salchow) in competition She first completed the

jump at the 2002 ISU Junior Grand Prix Final in the Netherlands at age 15

A bit on centripetal forcehellip

Centripetal force (FC) keeps an object moving along a curved path (rotating) Also centripetal force produces the centripetal component of acceleration

Fc = mac = m(v2 r) = m ωωωω2 r

Newtonrsquos Third Law

For every torque exerted by one

body (or body segment) on another body (or body segment) there is an equal and opposite

torque that is exerted by the second body (or body segment) on the first body (or body

segment)

Newtonrsquos Laws of Motion Angular Analogues

Newtonrsquos Third Law

Within our context this is

helpful to consider as we think about body segments apply torques to one

anotherhellip

Newtonrsquos Laws of Motion Angular Analogues

Summarybull Angular inertia (I) depends on (1) mass and (2)

mass location relative to the axis of rotation

bull Angular momentum H = I ω

bull In the absence of external torques H is conserved

bull Angular impulse is required to change H

bull ΣT = Iα

bull For every torque there is an equal and opposite torque

bull Centripetal force is required for an object to rotate

bull See both tables onlinehellip

Practicehellip

Answer each configuration has ~70 units of angular momentum

6

A 727 kg shot makes seven complete revolutions during its 25 second flight If its radius of gyration is 254 cm what is its angular momentum

a 00825 kgmiddotm2sb 738 kgmiddotm2sc 4616 kgmiddotm2sd None of the above

A 727 kg shot makes seven complete revolutions during its 25 second flight Its radius of gyration is 254 cm

What would happen to ω if the ball

had more m while conserving H

Answer It would decrease

What would happen to H if ω and

k were increased

Answer It would increase

A 727 kg hammer on a 1 m wire is released with a linear velocity of 28 ms What reaction force is exerted on the thrower by the hammer at the instant before release

a 05 Nb 1000 Nc 1604 Nd None of the above

A 727 kg hammer on a 1 m wire is rotated at a linear velocity of 28 ms

What force and corresponding component of acceleration are associated with this change in the direction of linear velocity Answer Centripetal force and centripetal or radial acceleration

What component of acceleration is associated with a potential change in the linear speed Answer Tangential acceleration

2

ApplicationsWhy would someone choke up on a bat use an aluminum bat or illegally cork a wooden bat Is there a legal alternative

Applications

Applications

Tuck vs Layout for a diver or gymnast

A runners leg during swing phase

tucklayout

hip

Angular analogues for Newtonrsquos Laws of Motion

Newtonrsquos First Law

A rotating body will maintain a state of constant rotational motion unless acted on by an external torque

This is the basis for the principle of conservation of angular momentum (H)

What is Angular Momentum (H)

Momentum

bull For linear motion L = mv

bull For angular motion H = I ωωωω

Or H = (mk2) ωωωω

bull Factors that affect angular momentum (H)

ndash mass of the object (m)

ndash location of mass relative to axis or rotation (k)

ndash angular velocity of the object (ωωωω)

Units for angular momentum kgsdotsdotsdotsdotm2

s

Conservation of Angular Momentum (H)

Similar to L H for any given system remains constant in the absence of a net external

torque

However unlike the linear circumstances we discussed I and ω can change

So we cannot assume that either I or ω are conserved

throughout flight

3

Conserving Angular MomentumExample Problem A 60-kg diver is in a layout position (k = 05 m) immediately after leaving the board with an angular velocity of 4 rads What is the diverrsquos angular velocity when he assumes a

tuck position and reduces his radius of gyration to 025 m

k = 05 m

k = 025 m

Conservation of Angular Momentum

First find H when diver leaves the board

H = mk2ωωωω

H = (60 kg)(05 m)2(4 rads) = 60 kgsdotsdotsdotsdotm2s

H is constant so now find ωωωω when k is reduced to 025 m

60 kgsdotsdotsdotsdotm2s = (60 kg)(025 m)2 ωωωω

ωωωω = 16 rads

Falling cats

H about the long axis of the cat is initially zero and must be conserved throughout flight however the cat always rights itself How

Video Link

Although total body angular momentum is

conserved while the body is airborne (no external torques)

angular momentum can be transferred between body segments

Transfer of Angular Momentum

Also although total body angular momentum is conserved while the body is airborne (no

external torques) one can also change the total body axis of rotation (eg

a forward roll can become a twist)

Transfer of Angular MomentumFinally although angular momentum can be

transferred between body segments or the whole-body axis of rotation may changehellip

the whole-body center of mass must still follow a

parabolic trajectory while the body is airborne

4

Newtonrsquos Second Law

Torque causes angular acceleration as well as ∆H for a body that is directly proportional to

the magnitude of torque in the same direction as the torque and inversely proportional to

the bodyrsquos moment of inertia

ΣT = I αααα (compare with ΣF = m a)

Newtonrsquos Laws of Motion Angular Analogues

Net joint torque and knee pain

A Practice Problem The Answer

Angular Impulse amp Momentum

How does a person change H

external torque

Force torque and linear and angular impulse

ndash Linear Impulse = force timestimestimestimes time = F ∆∆∆∆ t

ndash Angular Impulse = torque timestimestimestimes time = T ∆∆∆∆ t

Impulse-momentum relationship

ndash Linear F ∆∆∆∆ t = ∆∆∆∆M F t = (mv)2 ndash (mv)1

ndash Angular T ∆∆∆∆ t = ∆∆∆∆H T t = (I ωωωω)2 ndash (I ωωωω)1

Practice ProblemsTo initiate a twisting jump Miki applies a force to the ice that results in a torque about her long axis Consequently H (about her long axis) increases from 0 to 50 kgmiddotm2s in 025 s During this time I (about her long axis) is 22 kgmiddotm2

1How large was the associated angular impulse (AI) Answer 50 Nmmiddots

2How large was the associated torque Answer 200 Nm

3How fast is Mikirsquos angular velocity (about her long axis) at the end of the 025 s Answer 227 rads or 316 revs

Miki Ando is one of a few female skaters to have landed a quadruple

jump (a salchow) in competition She first completed the jump at the 2002

ISU Junior Grand Prix Final in the Netherlands at age 15

5

Practice ProblemsIn order to rotate four times in the air during a single jump Miki must increase ω about her long axis

1 How can Miki manipulate I (about her long axis)

2 Is it beneficial for Miki to manipulate I (about her long axis) If so why

3 What might the overall effect of an increased or decreased I (about her long axis) be on her final score

Japanese figure skater Miki Ando is the only female skater to have landed a

quadruple jump (a salchow) in competition She first completed the

jump at the 2002 ISU Junior Grand Prix Final in the Netherlands at age 15

A bit on centripetal forcehellip

Centripetal force (FC) keeps an object moving along a curved path (rotating) Also centripetal force produces the centripetal component of acceleration

Fc = mac = m(v2 r) = m ωωωω2 r

Newtonrsquos Third Law

For every torque exerted by one

body (or body segment) on another body (or body segment) there is an equal and opposite

torque that is exerted by the second body (or body segment) on the first body (or body

segment)

Newtonrsquos Laws of Motion Angular Analogues

Newtonrsquos Third Law

Within our context this is

helpful to consider as we think about body segments apply torques to one

anotherhellip

Newtonrsquos Laws of Motion Angular Analogues

Summarybull Angular inertia (I) depends on (1) mass and (2)

mass location relative to the axis of rotation

bull Angular momentum H = I ω

bull In the absence of external torques H is conserved

bull Angular impulse is required to change H

bull ΣT = Iα

bull For every torque there is an equal and opposite torque

bull Centripetal force is required for an object to rotate

bull See both tables onlinehellip

Practicehellip

Answer each configuration has ~70 units of angular momentum

6

A 727 kg shot makes seven complete revolutions during its 25 second flight If its radius of gyration is 254 cm what is its angular momentum

a 00825 kgmiddotm2sb 738 kgmiddotm2sc 4616 kgmiddotm2sd None of the above

A 727 kg shot makes seven complete revolutions during its 25 second flight Its radius of gyration is 254 cm

What would happen to ω if the ball

had more m while conserving H

Answer It would decrease

What would happen to H if ω and

k were increased

Answer It would increase

A 727 kg hammer on a 1 m wire is released with a linear velocity of 28 ms What reaction force is exerted on the thrower by the hammer at the instant before release

a 05 Nb 1000 Nc 1604 Nd None of the above

A 727 kg hammer on a 1 m wire is rotated at a linear velocity of 28 ms

What force and corresponding component of acceleration are associated with this change in the direction of linear velocity Answer Centripetal force and centripetal or radial acceleration

What component of acceleration is associated with a potential change in the linear speed Answer Tangential acceleration

3

Conserving Angular MomentumExample Problem A 60-kg diver is in a layout position (k = 05 m) immediately after leaving the board with an angular velocity of 4 rads What is the diverrsquos angular velocity when he assumes a

tuck position and reduces his radius of gyration to 025 m

k = 05 m

k = 025 m

Conservation of Angular Momentum

First find H when diver leaves the board

H = mk2ωωωω

H = (60 kg)(05 m)2(4 rads) = 60 kgsdotsdotsdotsdotm2s

H is constant so now find ωωωω when k is reduced to 025 m

60 kgsdotsdotsdotsdotm2s = (60 kg)(025 m)2 ωωωω

ωωωω = 16 rads

Falling cats

H about the long axis of the cat is initially zero and must be conserved throughout flight however the cat always rights itself How

Video Link

Although total body angular momentum is

conserved while the body is airborne (no external torques)

angular momentum can be transferred between body segments

Transfer of Angular Momentum

Also although total body angular momentum is conserved while the body is airborne (no

external torques) one can also change the total body axis of rotation (eg

a forward roll can become a twist)

Transfer of Angular MomentumFinally although angular momentum can be

transferred between body segments or the whole-body axis of rotation may changehellip

the whole-body center of mass must still follow a

parabolic trajectory while the body is airborne

4

Newtonrsquos Second Law

Torque causes angular acceleration as well as ∆H for a body that is directly proportional to

the magnitude of torque in the same direction as the torque and inversely proportional to

the bodyrsquos moment of inertia

ΣT = I αααα (compare with ΣF = m a)

Newtonrsquos Laws of Motion Angular Analogues

Net joint torque and knee pain

A Practice Problem The Answer

Angular Impulse amp Momentum

How does a person change H

external torque

Force torque and linear and angular impulse

ndash Linear Impulse = force timestimestimestimes time = F ∆∆∆∆ t

ndash Angular Impulse = torque timestimestimestimes time = T ∆∆∆∆ t

Impulse-momentum relationship

ndash Linear F ∆∆∆∆ t = ∆∆∆∆M F t = (mv)2 ndash (mv)1

ndash Angular T ∆∆∆∆ t = ∆∆∆∆H T t = (I ωωωω)2 ndash (I ωωωω)1

Practice ProblemsTo initiate a twisting jump Miki applies a force to the ice that results in a torque about her long axis Consequently H (about her long axis) increases from 0 to 50 kgmiddotm2s in 025 s During this time I (about her long axis) is 22 kgmiddotm2

1How large was the associated angular impulse (AI) Answer 50 Nmmiddots

2How large was the associated torque Answer 200 Nm

3How fast is Mikirsquos angular velocity (about her long axis) at the end of the 025 s Answer 227 rads or 316 revs

Miki Ando is one of a few female skaters to have landed a quadruple

jump (a salchow) in competition She first completed the jump at the 2002

ISU Junior Grand Prix Final in the Netherlands at age 15

5

Practice ProblemsIn order to rotate four times in the air during a single jump Miki must increase ω about her long axis

1 How can Miki manipulate I (about her long axis)

2 Is it beneficial for Miki to manipulate I (about her long axis) If so why

3 What might the overall effect of an increased or decreased I (about her long axis) be on her final score

Japanese figure skater Miki Ando is the only female skater to have landed a

quadruple jump (a salchow) in competition She first completed the

jump at the 2002 ISU Junior Grand Prix Final in the Netherlands at age 15

A bit on centripetal forcehellip

Centripetal force (FC) keeps an object moving along a curved path (rotating) Also centripetal force produces the centripetal component of acceleration

Fc = mac = m(v2 r) = m ωωωω2 r

Newtonrsquos Third Law

For every torque exerted by one

body (or body segment) on another body (or body segment) there is an equal and opposite

torque that is exerted by the second body (or body segment) on the first body (or body

segment)

Newtonrsquos Laws of Motion Angular Analogues

Newtonrsquos Third Law

Within our context this is

helpful to consider as we think about body segments apply torques to one

anotherhellip

Newtonrsquos Laws of Motion Angular Analogues

Summarybull Angular inertia (I) depends on (1) mass and (2)

mass location relative to the axis of rotation

bull Angular momentum H = I ω

bull In the absence of external torques H is conserved

bull Angular impulse is required to change H

bull ΣT = Iα

bull For every torque there is an equal and opposite torque

bull Centripetal force is required for an object to rotate

bull See both tables onlinehellip

Practicehellip

Answer each configuration has ~70 units of angular momentum

6

A 727 kg shot makes seven complete revolutions during its 25 second flight If its radius of gyration is 254 cm what is its angular momentum

a 00825 kgmiddotm2sb 738 kgmiddotm2sc 4616 kgmiddotm2sd None of the above

A 727 kg shot makes seven complete revolutions during its 25 second flight Its radius of gyration is 254 cm

What would happen to ω if the ball

had more m while conserving H

Answer It would decrease

What would happen to H if ω and

k were increased

Answer It would increase

A 727 kg hammer on a 1 m wire is released with a linear velocity of 28 ms What reaction force is exerted on the thrower by the hammer at the instant before release

a 05 Nb 1000 Nc 1604 Nd None of the above

A 727 kg hammer on a 1 m wire is rotated at a linear velocity of 28 ms

What force and corresponding component of acceleration are associated with this change in the direction of linear velocity Answer Centripetal force and centripetal or radial acceleration

What component of acceleration is associated with a potential change in the linear speed Answer Tangential acceleration

4

Newtonrsquos Second Law

Torque causes angular acceleration as well as ∆H for a body that is directly proportional to

the magnitude of torque in the same direction as the torque and inversely proportional to

the bodyrsquos moment of inertia

ΣT = I αααα (compare with ΣF = m a)

Newtonrsquos Laws of Motion Angular Analogues

Net joint torque and knee pain

A Practice Problem The Answer

Angular Impulse amp Momentum

How does a person change H

external torque

Force torque and linear and angular impulse

ndash Linear Impulse = force timestimestimestimes time = F ∆∆∆∆ t

ndash Angular Impulse = torque timestimestimestimes time = T ∆∆∆∆ t

Impulse-momentum relationship

ndash Linear F ∆∆∆∆ t = ∆∆∆∆M F t = (mv)2 ndash (mv)1

ndash Angular T ∆∆∆∆ t = ∆∆∆∆H T t = (I ωωωω)2 ndash (I ωωωω)1

Practice ProblemsTo initiate a twisting jump Miki applies a force to the ice that results in a torque about her long axis Consequently H (about her long axis) increases from 0 to 50 kgmiddotm2s in 025 s During this time I (about her long axis) is 22 kgmiddotm2

1How large was the associated angular impulse (AI) Answer 50 Nmmiddots

2How large was the associated torque Answer 200 Nm

3How fast is Mikirsquos angular velocity (about her long axis) at the end of the 025 s Answer 227 rads or 316 revs

Miki Ando is one of a few female skaters to have landed a quadruple

jump (a salchow) in competition She first completed the jump at the 2002

ISU Junior Grand Prix Final in the Netherlands at age 15

5

Practice ProblemsIn order to rotate four times in the air during a single jump Miki must increase ω about her long axis

1 How can Miki manipulate I (about her long axis)

2 Is it beneficial for Miki to manipulate I (about her long axis) If so why

3 What might the overall effect of an increased or decreased I (about her long axis) be on her final score

Japanese figure skater Miki Ando is the only female skater to have landed a

quadruple jump (a salchow) in competition She first completed the

jump at the 2002 ISU Junior Grand Prix Final in the Netherlands at age 15

A bit on centripetal forcehellip

Centripetal force (FC) keeps an object moving along a curved path (rotating) Also centripetal force produces the centripetal component of acceleration

Fc = mac = m(v2 r) = m ωωωω2 r

Newtonrsquos Third Law

For every torque exerted by one

body (or body segment) on another body (or body segment) there is an equal and opposite

torque that is exerted by the second body (or body segment) on the first body (or body

segment)

Newtonrsquos Laws of Motion Angular Analogues

Newtonrsquos Third Law

Within our context this is

helpful to consider as we think about body segments apply torques to one

anotherhellip

Newtonrsquos Laws of Motion Angular Analogues

Summarybull Angular inertia (I) depends on (1) mass and (2)

mass location relative to the axis of rotation

bull Angular momentum H = I ω

bull In the absence of external torques H is conserved

bull Angular impulse is required to change H

bull ΣT = Iα

bull For every torque there is an equal and opposite torque

bull Centripetal force is required for an object to rotate

bull See both tables onlinehellip

Practicehellip

Answer each configuration has ~70 units of angular momentum

6

A 727 kg shot makes seven complete revolutions during its 25 second flight If its radius of gyration is 254 cm what is its angular momentum

a 00825 kgmiddotm2sb 738 kgmiddotm2sc 4616 kgmiddotm2sd None of the above

A 727 kg shot makes seven complete revolutions during its 25 second flight Its radius of gyration is 254 cm

What would happen to ω if the ball

had more m while conserving H

Answer It would decrease

What would happen to H if ω and

k were increased

Answer It would increase

A 727 kg hammer on a 1 m wire is released with a linear velocity of 28 ms What reaction force is exerted on the thrower by the hammer at the instant before release

a 05 Nb 1000 Nc 1604 Nd None of the above

A 727 kg hammer on a 1 m wire is rotated at a linear velocity of 28 ms

What force and corresponding component of acceleration are associated with this change in the direction of linear velocity Answer Centripetal force and centripetal or radial acceleration

What component of acceleration is associated with a potential change in the linear speed Answer Tangential acceleration

5

Practice ProblemsIn order to rotate four times in the air during a single jump Miki must increase ω about her long axis

1 How can Miki manipulate I (about her long axis)

2 Is it beneficial for Miki to manipulate I (about her long axis) If so why

3 What might the overall effect of an increased or decreased I (about her long axis) be on her final score

Japanese figure skater Miki Ando is the only female skater to have landed a

quadruple jump (a salchow) in competition She first completed the

jump at the 2002 ISU Junior Grand Prix Final in the Netherlands at age 15

A bit on centripetal forcehellip

Centripetal force (FC) keeps an object moving along a curved path (rotating) Also centripetal force produces the centripetal component of acceleration

Fc = mac = m(v2 r) = m ωωωω2 r

Newtonrsquos Third Law

For every torque exerted by one

body (or body segment) on another body (or body segment) there is an equal and opposite

torque that is exerted by the second body (or body segment) on the first body (or body

segment)

Newtonrsquos Laws of Motion Angular Analogues

Newtonrsquos Third Law

Within our context this is

helpful to consider as we think about body segments apply torques to one

anotherhellip

Newtonrsquos Laws of Motion Angular Analogues

Summarybull Angular inertia (I) depends on (1) mass and (2)

mass location relative to the axis of rotation

bull Angular momentum H = I ω

bull In the absence of external torques H is conserved

bull Angular impulse is required to change H

bull ΣT = Iα

bull For every torque there is an equal and opposite torque

bull Centripetal force is required for an object to rotate

bull See both tables onlinehellip

Practicehellip

Answer each configuration has ~70 units of angular momentum

6

A 727 kg shot makes seven complete revolutions during its 25 second flight If its radius of gyration is 254 cm what is its angular momentum

a 00825 kgmiddotm2sb 738 kgmiddotm2sc 4616 kgmiddotm2sd None of the above

A 727 kg shot makes seven complete revolutions during its 25 second flight Its radius of gyration is 254 cm

What would happen to ω if the ball

had more m while conserving H

Answer It would decrease

What would happen to H if ω and

k were increased

Answer It would increase

A 727 kg hammer on a 1 m wire is released with a linear velocity of 28 ms What reaction force is exerted on the thrower by the hammer at the instant before release

a 05 Nb 1000 Nc 1604 Nd None of the above

A 727 kg hammer on a 1 m wire is rotated at a linear velocity of 28 ms

What force and corresponding component of acceleration are associated with this change in the direction of linear velocity Answer Centripetal force and centripetal or radial acceleration

What component of acceleration is associated with a potential change in the linear speed Answer Tangential acceleration

6

A 727 kg shot makes seven complete revolutions during its 25 second flight If its radius of gyration is 254 cm what is its angular momentum

a 00825 kgmiddotm2sb 738 kgmiddotm2sc 4616 kgmiddotm2sd None of the above

A 727 kg shot makes seven complete revolutions during its 25 second flight Its radius of gyration is 254 cm

What would happen to ω if the ball

had more m while conserving H

Answer It would decrease

What would happen to H if ω and

k were increased

Answer It would increase

A 727 kg hammer on a 1 m wire is released with a linear velocity of 28 ms What reaction force is exerted on the thrower by the hammer at the instant before release

a 05 Nb 1000 Nc 1604 Nd None of the above

A 727 kg hammer on a 1 m wire is rotated at a linear velocity of 28 ms

What force and corresponding component of acceleration are associated with this change in the direction of linear velocity Answer Centripetal force and centripetal or radial acceleration

What component of acceleration is associated with a potential change in the linear speed Answer Tangential acceleration