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.

 

[rwisz]

for your question! Your solution for part a is correct. To confirm, you can also use the formula for angular acceleration, which is change in angular velocity divided by time. In this case, the change in angular velocity is 33.33 rev/min (converted to 3.49 rad/s) and the time is 20.0 s, which gives the same result of 0.175 rad/s^2.

For part b, your approach is correct but there is a minor mistake in your calculation. The angular displacement should be 69.8 rad, but when converting to revolutions, you need to divide by 2π to get the number of revolutions. So the correct answer would be 69.8 rad / 2π = 11.1 revolutions. Great job overall!