Physics Angular Acceleration Daniel H and Jayson

7/29/2019 Physics Angular Acceleration Daniel H and Jayson

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Uniform Circular Motion and

Gravitation discussed only uniform

circular motion, which is motion in

a circle at constant speed and,

hence, constant

angular velocity. Recall that angular

velocity was defined as the time

rate of change of angle :


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= /tFigure 1.1

where is the angle of rotationas seen in Figure 1.1. The

relationship between angular

velocity and linear velocity vwas also defined in

Rotation Angle and Angular

Velocity as v=r (10.2)


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= /tFigure 1.1

Or =vrwhere r is the radius of curvature.

According to the sign convention,

the counter clockwise direction is

considered as

positive direction and clockwise

direction as negative


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Figure 1.2 This figure shows uniform circular

motion and some of its defined quantities.


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Angular velocity is not constant

when a skater pulls in her arms,when a child starts up a merry-

go-round from rest, or when a

computers hard diskslows to a halt when switched off.

In all these cases, there is an

angular acceleration ,


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Where,

=change in angular velocity

t=change in time.

The units of angular acceleration

are (rad/s)/s , or rad/s2 . If increases, then is positive. If

decreases, then is negative.

= /tFigure 1.3


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Suppose a teenager puts her bicycle on

its back and starts the rear wheel

spinning from rest to a final angularvelocity of 250 rpm in 5.00 s. (a)

Calculate the angular acceleration in

rad/s2 . (b) If she now slams on thebrakes, causing an angular acceleration

of 87.3 rad/s2 , how long

does it take the wheel to stop?


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Entering known

information into thedefinition of angular

acceleration, we get

=/t

= 250 rpm/5.00 s .


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Because is in revolutions per

minute (rpm) and we want thestandard units of rad/s2 for angular

acceleration, we need to convert

from rpm to rad/s:

=250 rev/min

2rad/rev

1min/60

sec

=26.2rasd.


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Entering this quantity into

the expression for , we

get

= w/t

=[ (26.2 rad/s)/(5.00 s) ]

= 5.24 rad/s2.


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Here the angular velocity decreases

from 26.2 rad/s (250 rpm) to zero,so that is 26.2 rad/s , and is

given to be 87.3 rad/s2 .

Thus,t = (26.2 rad/s) / ( 87.3 rad/s2)

= 0.300 s.


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Note that the angular acceleration as the girlspins the wheel is small and positive; it takes

5 s to produce an appreciable angular

velocity. When she hits the brake, the

angular acceleration is large and negative.

The angular velocity quickly goes to zero. In

both cases, the relationships are analogous

to what happens with linear motion. Forexample, there is a large deceleration when

you crash into a brick wallthe velocity

change is large in a short time interval.


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Physics Angular Acceleration Daniel H and Jayson

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