pptg101213 rotational motions gallego

7/30/2019 PPTG101213 Rotational Motions GALLEGO

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In the picture are three gears.

Each gears rotation causes

rotation of another.

Suppose the radius of purple, yellow and red gears

are x, 2x, and 3x respectively, by how much faster

or slower does the purple gear rotate comparedto red?

Rotational Motion


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Rotational, Linear & Angular Velocity

If the disc will make one complete rotation in 1 second,

which point (A, B, or C) moves the fastest?

x

A

2x

B

3x

C


When the disc makes a complete rotation, how are you

going to determine the distance it covers?

How are the distances covered by A compared to that

of B and C?


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When the disc make a quarter turn from Position 1 to Position 2,

points A, B and C will also move and align to the final position.

If the displacement (d) is extended into straight path, the lineardisplacement of C is obviously the longer. While moving at equal

time with others, it is moving the fastest. That speed is called

linear speed (v).

1

2


In some respect, the three points move together at the same

time. The change of position can be reflected by the change in

angle--- which the three show the same change.

The change in angle in a given amount of time is calledangular

speed ( )

1

2


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Notice that the angular speedof the three are the same. But the

distance covered by point C is the greatest. Notice also the

distance of C from the axis of rotation (radius), it is the farthest.Therefore, the farther is the object from the center, the bigger is

the distance (d) covered.

1

2

In the picture are three gears.

Each gears rotation causes

rotation of another.

Suppose the radius of purple, yellow and red gears

are x, 2x, and 3x respectively, by how much faster

or slower does the purple gear rotate compared

to red?


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Consider a disc with a radius of 2 meters. The length of its edge(circumference) is measured by the counter. When one complete

revolution has elapsed, what reading will be registered in the

counter?

r=2m 0.0m


When the disc rolls on the ground, one complete revolution of it

will cover a distance similar to its diameter.

How far does a disc of diameter 2m cover after rolling at a speed

of 60rpm in 1 minute?

r=2m 0.0m


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Getting the relationship of all:

S r

t

Sv

t

S

v

r

r

t t

S rt

Rotational, Linear & Angular Velocity (Problems)A pair of identical 1000-kg space pods in outer space

are connected to each other by a 900-m-long cable.

They rotate about a common point like a spinning

dumbbell at 1.2 rpm. What is its angular velocity?

(rad/s)

.

t

rev

1 2

min rev

2 min1

.

s

rad

s

60

0 13


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Rotational, Linear & Angular Velocity (Problems)

A calesa with wheels whose diameter is 1.5 meters is

traveling at 24 kph. Find the angular velocity of thewheel in revolutions per minute.

Pretend that it only travels for one hour. Then calesa would have traveled

24km or 24000m.

When the calesa makes one rotation it would travel the distance of its

circumference.

S= r

or

= D

= 1.5

=4.71m

r

2

S is the circumference

D is the diameter

This is the distance traveled by

the calesa wheel per rotation.

Rotational, Linear & Angular Velocity (Problems)A calesa with wheels whose diameter is 1.5 meters is

traveling at 24 kph. Find the angular velocity of the

wheel in revolutions per minute.

total distance traveled

no. of rotations= distance covered per rotation

.

. rotations

m

rotation

m24000

4 71

5095 5


24km or 24000m.


circumference.

This is the total number of

rotations made by calesa

wheel in 1 hour or 60 minutes.


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Rotational, Linear & Angular Velocity (Problems)

A calesa with wheels whose diameter is 1.5 meters is

traveling at 24 kph. Find the angular velocity of thewheel in revolutions per minute.

5095.5 rev 1hour=

hour 60min

.min

rev

84 9


24km or 2400m.


circumference.

The wheel of diameter 1.5m

can make this much of

rotation every minute orrpm.

Angular Acceleration

When a disc begins to rotate, its initial rotational velocity is zero,therefore, its angular velocity is also zero.

When it rotates, it will gain rotational speed at increasing rate

until it reaches its desired rpm.

During this time of gaining rotational speed, the angular speed

also changes. Therefore we say that it has angular acceleration.


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Angular Acceleration

Did you notice that when the angle changes rapidly, the linear

displacement also changes rapidly?

When the rotation is accelerating angularly, the movement is

also accelerating linearly.

vr

t t

a r

Angular AccelerationIn constant angular

acceleration

f i

t

In constant linear

acceleration

f iv v

at

f it

2

f iv v

d t2

itt

2

2i

atd v t

2

2

f i

2 2

2

f iv v

da

2 2

2


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Angular Acceleration (Problems)

When a record player is stopped, the turn table, initially

rotating at 33.3rpm, slows down and stop in 60s.Calculate the angular acceleration of the turn table.

=t

.=

60s

.

f i

rad

s

rad

s

2

0 3 49

0 058

. min=

min

.=

60s

.

rev

rev s

rad

rad

s

33 3 2 1

60

209 23

3 49

Angular Acceleration (Problem)When the rotational speed of a rotating object changes

from 2rpm to 3rpm in 30s, how much does it

accelerate? Express your answer in (rad/s2).

=

=

t

rev

1

min

. rad

rev

6 28

1

min1

.

ss

rad

s2

60

30

0 00349


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Angular Acceleration (Problem)

A Ferris wheel starts from rest and acquires an angular

velocity of 0.5rad/s after completing one revolution.Calculate the distance covered by the person seated

20m from the axis of rotation.

.

.

S r

r

m

m

2

6 28 20

125 6

Rotational Inertia

A B

Which is easier to balance? Why?


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Rotational Inertia

As linear inertia is a bodys resistance to change in motion,

rotational inertia is the bodys resistance to change in rotation.

In linear inertia, change in motion is caused by a net force

In rotational inertia, change in rotation is caused by a net torque.

Linear inertia is bigger when mass is bigger.

Rotational inertia is bigger when the distance between center of

mass and axis of rotation is bigger.

Rotational Inertia

Explain why a barbell with

weights near the hand easy

to rotate that the one with

weights far from the hand?


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Rotational Inertia

How can a long pole help atight rope walker?

Rotational Inertia

Which disc will roll faster?

Why? A B


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Angular Momentum

A mass that moves in a straight path has linear momentum that can

derived as a product oflinear inertia (mass) and linear velocity.

p=mv

A mass that rotates has angular momentum which can be derived as

a product ofrotational inertia and angular velocity.

L=I

Angular Momentum (Problem)

A mass that moves in a straight path has linear momentum that can

derived as a product oflinear inertia (mass) and linear velocity.

p=mv

A mass that rotates has angular momentum which can be derived asa product ofrotational inertia and angular velocity.

L=I


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Conservation of Angular Momentum (Problem)

A pair of identical 1000-kg space pods in outer space

are connected to each other by a 900-m-long cable.They rotate about a common point like a spinning

dumbbell at 1.2 rpm. If one of the pods pulls in 100m

of cable what will be the systems new rotation rate?bef ore afte r

b ef or e b ef or e a ft er a ft er

L L

I I

m

before beforer m

2

.

.

after after

before before

after

after

r

r

r

m rpm

m

rpm

2

2

2

2

2

450 1 2

400

1 5

m recurs in both sides of the equation so it can be

omitted.

When the diameter is reduced by 100m,

the radius will be reduced by only 50m.

If there are errors in the presentation, please feel free to

comment.

pptg101213 rotational motions gallego

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