Rotational motion of a turntable

[mizzy]

Homework Statement

The turntable of a record player rotates at 33.33rev/min and takes 20.0s to reach this speed from rest. Calculate: a) its angular acceleration, b) the number of revolutions it makes before reaching its final speed.

Homework Equations

angular acceleration = angular speed/ time
1 rev = 2pie rad
angular displacement = angular speed x time

The Attempt at a Solution

part a:
I converted the angular speed to rad/s. I solved for angular acceleration, which is delta angular speed divided by time.

3.49rad/s / 20.0s = 0.175 rad/s^2 Is that correct?

part b:
I used the equation, angular speed = angular displacement/time.

therefore, angular displacement = angular speed x time
3.49rad/s x 20.0s = 69.8rad

I then converted rad into revolutions --> 11.1 revolutions. Is that correct??


Thanks

 

[Gear.0]

Part A is correct.

For part B you're on the right track, but remember that would only work if the record were spinning at a constant speed of 3.49rad/s. But it is always changing as it goes from 0rad/s up to 3.49rad/s.

You want to do basically the same thing you did, except in place of 3.49rad/s you want to use the average angular velocity.

 

[mizzy]

Thanks.

So for part b, average angular velocity will be 3.49/2 = 1.75 rad/s.

therefore, angular displacement = 1.75 x 20.0 = 35 rad --> 5.57 revolutions.

 

[Gear.0]

Yup, that's it :D

Although, technically if you round here it would be 1.74 rad/s because of the round even rule, that many people are unaware of.
But don't mind that lol, the answer is right.