chapter 10 rotational kinematics and energy · microsoft powerpoint - peng10_lectureoutline.ppt...

Copyright © 2010 Pearson Education, Inc.

Chapter 10

Rotational Kinematics and Energy


Units of Chapter 10• Angular Position, Velocity, and Acceleration

• Rotational Kinematics

• Connections Between Linear and Rotational Quantities

•Rolling Motion

• Rotational Kinetic Energy and the Moment of Inertia

• Conservation of Energy


10-1 Angular Position, Velocity, and Acceleration

1 rev = 2π rad

2π rad = 360o

1 rad = 360o/ 2π = 57.3o



Degrees and revolutions:

= 2π rad

Q: Sign of θ here?



Arc length s, measured in radians:

Q: Why do we define 1 rev = 2π rad?A: The circumference of a circleC = 2π r

the angle for 1rev is C/r = 2π rad

s = r θ



Note: the sign of ω

Question 10.1aQuestion 10.1a Bonnie and Bonnie and KlydeKlyde II

ω

BonnieBonnieKlydeKlyde

Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every2 seconds.Klyde’s angular velocity is:

a) same as Bonnie’sb) twice Bonnie’sc) half of Bonnie’sd) one-quarter of Bonnie’se) four times Bonnie’s

The angular velocityangular velocity ωω of any point on a solid object rotating about a fixed axis is the sameis the same. Both Bonnie and Klyde go around one revolution (2π radians) every 2 seconds.

Question 10.1aQuestion 10.1a Bonnie and Bonnie and KlydeKlyde II

ω


Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every2 seconds.Klyde’s angular velocity is:

a) same as Bonnie’sb) twice Bonnie’sc) half of Bonnie’sd) one-quarter of Bonnie’se) four times Bonnie’s

Hint: angular velocity has a sign, negative or positive?



Ask: why?


10-2 Rotational Kinematics

If the angular acceleration is constant:


10-2 Rotational Kinematics

Analogies between linear and rotational kinematics:


below

An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θin the time t, through what angle did it rotate in the time t?

a) θb) θc) θd) 2 θe) 4 θ

Question 10.3aQuestion 10.3a Angular Displacement IAngular Displacement I

½

¼

¾

½

An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θin the time t, through what angle did it rotate in the time t?

a) θb) θc) θd) 2 θe) 4 θ

The angular displacement is θ = αt 2 (starting from rest), and there is a quadratic dependence on time. Therefore, in half the half the timetime, the object has rotated through oneone--quarter the anglequarter the angle.

Question 10.3aQuestion 10.3a Angular Displacement IAngular Displacement I

12

½

¼

¾

½

An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity ωat time t, what was its angular velocity at the time t?

a) ½ ω

b) ¼ ω

c) ¾ ω

d) 2 ωe) 4 ω

Question 10.3bQuestion 10.3b Angular Displacement IIAngular Displacement II

½

An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity ωat time t, what was its angular velocity at the time t?

The angular velocity is ω = αt (starting from rest), and there is a linear dependence on time. Therefore, in half the timehalf the time, the object has accelerated up to only half the speedhalf the speed.

Question 10.3bQuestion 10.3b Angular Displacement IIAngular Displacement II

a) ½ ω

b) ¼ ω

c) ¾ ω

d) 2 ωe) 4 ω

½


10-3 Connections Between Linear and Rotational Quantities

Q: derive this?

Question 10.1bQuestion 10.1b Bonnie and Bonnie and KlydeKlyde IIII

ω


a) Klydeb) Bonniec) both the samed) linear velocity is zero

for both of them

Bonnie sits on the outer rim of amerry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity?

Their linear speeds linear speeds vv will be

different because v = r v = r ωω and

Bonnie is located farther outBonnie is located farther out(larger radius r) than Klyde.

ω

BonnieBonnie

KlydeKlyde

BonnieKlyde V21V =

Question 10.1bQuestion 10.1b Bonnie and Bonnie and KlydeKlyde IIII

FollowFollow--upup:: Who has the larger centripetal acceleration?Who has the larger centripetal acceleration?

a) Klydeb) Bonniec) both the samed) linear velocity is zero

for both of them

Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity?



This merry-go-round has both tangential and centripetal acceleration.


(a)

(b)

Two methods


below


Summary of Chapter 10• Describing rotational motion requires analogs to position, velocity, and acceleration

• Average and instantaneous angular velocity:

• Average and instantaneous angular acceleration:


Summary of Chapter 10

• Period:

• Counterclockwise rotations are positive, clockwise negative

• Linear and angular quantities:


Summary of Chapter 10

• Linear and angular equations of motion:

Tangential speed:

Centripetal acceleration:

Tangential acceleration:

chapter 10 rotational kinematics and energy · microsoft powerpoint - peng10_lectureoutline.ppt...

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