Calculating Torque for LP Turntable with Given Angular Speed and Mass

[cstout]

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.

 

[Doc Al]

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

 

[cstout]

change in distance / change in time

 

[Doc Al]

change in distance / change in time

That's the definition of velocity. What's the similar definition of acceleration?

 

[cstout]

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

 

[Doc Al]

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.)

 

[cstout]

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]

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?