Angular acceleration and velocity in a circle

  • #1
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Homework Statement:

Use the following words to describe directions: "North", "South", "East", "West", "Up", and "Down"
Adam sits on the outer edge of a vinyl record, which has a radius R=6 inches. The record spins on a turntable at 33.33 RPM in a counterclockwise direction as seen from above. Adam loves going around in circles.
Alas, the record finishes playing, and the motor disengages. Over the next 21 seconds, the record gradually slows to a halt. You may assume that the angular acceleration is constant.

At time t=10 seconds after the motor disengages, Adam happens to be located directly East of the spindle. At this instant:
What is Adam's angular velocity? Give the magnitude and the direction.

What is Adam's linear velocity at this moment? Also give the direction (North, South, East, West)

What is Adam's angular acceleration at this moment? Just provide the magnitude.

What is the tangential linear acceleration of Adam? That is, what is the rate of change of his linear speed? You should be able to provide a direction this time.

What is Adam's centripetal acceleration at this moment?

Relevant Equations:

angular velocity=initial angular velocity + angular acceleration(time)
radius=6in=0.1524m
33.33 RPM (1min/60second)(6.28 radian/1 revolution) = 3.45 rad/s
linear velocity=3.45 rad/s * 0.1524m=0.526 m/s
linear acceleration= (0.526 m/s)^2 /(0.1524m)=1.814 m/s^2
1.814 m/s^2=(0.1524m)(rotational acceleration)
rotational acceleration=11.9 rad/s^2

ω1= (3.45 rad/s)+(11.9rad/s^2)(10s)
ω1=122.4 rad/s Up
 

Answers and Replies

  • #2
tnich
Homework Helper
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You seem to have confused rotational acceleration with centripetal acceleration. The problem states that the turntable slows to a stop at a constant rotational acceleration from 33RPM over 21 seconds. You can use that information and this equation to calculate the rotational acceleration:
Homework Equations: angular velocity=initial angular velocity + angular acceleration(time)
 
  • #3
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0=3.45 + (rotational acceleration)(21s)
rotational acceleration= -0.164 rad/s^2
|rotational acceleration|= 0.164 rad/s^2

ω1= (3.45 rad/s)+(-0.164 rad/s^2)(10s)
ω1= 1.81 rad/s Up

linear velocity = 1.81 rad/s * 0.1524m = 0.276 m/s North

linear acceleration = 0.164 rad/s^2 * 0.1524m= 25E-3m/s^2 South

centripetal acceleration= (0.276 m/s)^2 / 0.1524m=0.5m/s^2 West
 
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