How Do You Calculate the Angular Acceleration of a Decelerating Turntable?

[sterlinghubbard]

Problem:

The turntable of a record player rotates at a rate of 50.7 rev/min and takes 92.7s to come to rest when switched off.

Calculate the magnitude of its angular acceleration. Answer in units of rad/s^2.

Solution:

First I converted rev/min to rad/s. Which I got to be 5.309 rad/sec. Then I found the constant average decceleration which would be the decceleration because it is a constant decceleration.

A(avg)
=
The Change in Velocity
---------------------
The Change in Time

My soultion, which is wrong, is -.0573. What am I doing wrong?

 

[sterlinghubbard]

Ha!

Well, it was asking for the magnitude... so the solution was .0573 not -.0573.

 

[thepatientmental]

It seems like you are on the right track but your calculation for the average angular acceleration is incorrect. To find the average angular acceleration, we can use the formula:

α(avg) = (ωf - ωi) / t

Where:
α(avg) = average angular acceleration
ωf = final angular velocity (in rad/s)
ωi = initial angular velocity (in rad/s)
t = time (in seconds)

In this problem, ωf = 0 (since the turntable comes to rest) and ωi = 5.309 rad/s. Plugging in these values and the given time of 92.7 seconds, we get:

α(avg) = (0 - 5.309) / 92.7 = -0.0573 rad/s^2

So your calculation was correct, but you just forgot to include the negative sign in your answer. The negative sign indicates that the turntable is decelerating, as we would expect.

Therefore, the magnitude of the angular acceleration is 0.0573 rad/s^2.