# Homework Help: Circular Motion of a turntable

1. Nov 11, 2013

### Sylis

1. The problem statement, all variables and given/known data
A turntable rotates counterclockwise at 78rpm, a speck of dust on the turntable is at 0.42rad at t=0 ,What is the angle of the speck at t = 8.0s ? Your answer should be between 0 and 2π rad

2. Relevant equations
θfi=ωt

3. The attempt at a solution
I missed a couple of classes so I'm incredibly behind. I've been trying to google how to do things but it's not really working out for me, so if something is wrong let me know (which it obviously is or I wouldn't be here).

So, I started out by converting the 78 rpm measurement into an angular velocity

78rpm x 2∏ x 1/60 = 8.168rad/s

Then by using the formula for Δθ (θfi=ωt)
θf=ωt+θi

I've tried 66 rad and 65 rad just to see if that helped at all, but to no avail. I know it says that my answer is supposed to be between 0 and 2pi and that 65.5 is far larger than 2pi, what else am I supposed to do?

I've done my best at the problem... I don't know what else to do.

2. Nov 11, 2013

### nasu

A full rotation is 2∏ radians.
After a full rotation the speck is back where is was. So you need to find what is the closest multiple of 2∏ (but lower than your result) and take only what is left over.
For example if your result would be 10 radians, the closest multiple is 6.28 (2 ∏) so the angle of displacement will be 10-6.28= 3.72 rad.

3. Nov 11, 2013

### Sylis

I got it, 65.585- (2pi x 10) = 2.9 rad.

Thank you. I'm having a real tough time with these problems.