# Rotation of a rigid body

1. Sep 18, 2011

### Kurokari

1. The problem statement, all variables and given/known data

A turntable rotates at a uniform angular speed of 3.0 rads^-1. A record is dropped from rest onto the turntable. Initially the record skids on the turntable but eventually rotates together withe the turntable.

(a) While the record is skidding on the turntable, the angular displacement of the turntable is 0.20rad. Find the average angular acceleration of the record before it achieves the constant speed of the turntable.

2. Relevant equations

I'm writing this with reference to linear motion since the symbols used in rotational are a bit tedious to write, but I'm confident you will understand.

s = ut + [(1/2)at^2)
ωf=ωi+αt

3. The attempt at a solution

Actually I had some guidance, first that is to find the time of the turntable when it moved 0.2rad while the record was skidding.

Then time is substituted into the second equation I've given above to find the angular acceleration.

The problem is I don't understand what is the relation between the time taken for the turntable to travel 0.2rad and the angular acceleration of the record.

Last edited: Sep 18, 2011
2. Sep 18, 2011

### issacnewton

$$\omega_f=\omega_i+\alpha t$$

3. Sep 18, 2011

### issacnewton

$$\omega_f=\omega_i+\alpha t$$

4. Sep 18, 2011

### lewando

During this time (or equivalently, during this angular displacement) the record is sliding--a frictional force is being applied to the record, resulting in its acceleration. When the speed of the record increases to that of the turntable, it no longer slides (no longer is a frictional force causing acceleration) and so it maintains the same speed as the turntable. Hope this helps.

5. Sep 18, 2011

### Kurokari

So when the question says skidding, actually is the record moving?

@issacnewton thnks! I'm not too familiar with all the scripting, you're a fantastic help! =)

6. Sep 18, 2011

### lewando

Initially, it is not moving--"dropped from rest", yet upon contact with the turntable it begins to move (rotate). It starts at 0 rads/sec and increases until it acheives 3 rads/sec.