# Torque and angular speed

## Homework Statement

An LP turntable must spin at 3.53 rad/s to play a record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 1.9 revolutions, starting from rest? The turntable is a uniform disk of diameter 30.7 cm and mass 0.24 kg.

## Homework Equations

T=rF
F=ma
Theda = (Angular Acceleration (t^2)) / 2

## The Attempt at a Solution

I tried using the above equations but i'm not sure about finding the angular acceleration to find the the final Torque.

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Doc Al
Mentor
What's the most basic definition of acceleration? That's what you need here.

change in distance / change in time

Doc Al
Mentor
change in distance / change in time
That's the definition of velocity. What's the similar definition of acceleration?

oh yea, sorry, change in velocity / change in time

Doc Al
Mentor
oh yea, sorry, change in velocity / change in time
Good. So the angular acceleration is the change in angular velocity over time.

But I just realized that they didn't give you the time--I misread the problem. (D'oh!) So you'll need to use another approach to find the time.

Try this: What's the average speed of the turntable while it's accelerating? Use that--and the distance--to calculate the time. (Change revolutions to radians.)

Ok, so the Time = Distance / Average Speed, the distance is 11.932 radians, but what is the average speed, is it simply the given speed of 3.53 or something else?

Doc Al
Mentor
but what is the average speed, is it simply the given speed of 3.53 or something else?
No. 3.53 rad/s is the final speed and 0 is the initial speed. So what's the average speed?