# Homework Help: Rotating disk question.

1. Dec 23, 2012

### peripatein

Hi,
1. The problem statement, all variables and given/known data
A horizontal smooth disk of radius R rotates around its axis with constant speed ω. At t=0 a mass m is thrown at speed v0 (in the lab's frame of reference) towards the center of the disk.
I am asked to write down the velocity vector of the mass in the lab's frame of reference and in the disk's. It is stated that in both cases the origin is at the center of the disk.

2. Relevant equations

3. The attempt at a solution
Primarily, won't the mass's acceleration in the lab's frame of reference be:
a = -2ω x v' - ω x (ω x r), where |v| = v0 - ωr?

Won't the mass's velocity in the disk's frame of reference be:
v = [ωr]θ + [dr/dt]r?
I could truly use some guidance here. Thanks!

2. Dec 23, 2012

### rcgldr

The mass isn't accelerating, it's moving at constant velocity v0, from the lab's frame of reference.

3. Dec 23, 2012

### peripatein

Okay, so is -2ω x v' - ω x (ω x r)=0, where |v| = v0 - ωr?

4. Dec 23, 2012

### haruspex

In which frame?

5. Dec 26, 2012

### peripatein

Would it be correct to say that in the lab's reference frame, the velocity of the mass is:
V = [wr]θ+[wtv0]r?
Would it be correct to say that in the disk's reference frame, the velocity of the mass is:
V = [v0]θ

6. Dec 26, 2012

### peripatein

I would really appreciate some feedback on what I think the velocities would be in both reference frames.

7. Dec 26, 2012

### haruspex

Not sure I understand your notation. You're using polar co-ordinates for both frames, right? If so, I guess it's the same r for each, and theta's the same at t=0. The mass comes in along theta=0 in the lab's frame.
Given all that, why does the velocity in the lab's frame involve ω? And what would ωtv0 be... an angle multiplied by a speed?

8. Dec 26, 2012

### peripatein

So will the velocity, from an inertial frame's pov, simply be wr(t), where r=vrt?
Won't it then be wv_0*t?

9. Dec 26, 2012

### haruspex

As I understand the statement, the mass starts with speed v0 towards the origin, along the line θ=0, say. In polar, I guess you'd write that (-v0, 0). Since the disk is smooth, that won't change.

10. Dec 26, 2012

### peripatein

I am not sure I understand. My book claims that to an inertial observer the mass will be moving at constant speed along the radius, i.e. straight line, whereas from the disk's reference frame it will be moving at a speed equal to vr + w x r.
Would you disagree?

11. Dec 26, 2012

### rcgldr

So why do you include

[wtv0]r

as one of the terms?

In polar coordinates, dr/dt = v0, and dθ/dt = 0. θ would be a constant, while r = r0 + v0 t.