# Homework Help: Rotational motion

1. Jul 12, 2015

### Avaron Cooper

1. A ring , a disk and a sphere all of same mass and radius, with moments of inertia Ir, Id, Is respectively about their axes, roll down without slipping on an inclined plane from a given height. If the time taken for the ring, disk and sphere to reach the bottom of the plane are tr, td and ts respectively, then
1)tr<td<ts
2)tr=td=ts
3)tr>td>ts
4)tr>td=ts
5)tr>td<ts

2. Relevant equations
. torque=moment of inertia*angular acceleration

3. The attempt at a solution
I took the torque acting on the objects to be the same theefore moment of inertia to be indirectly proportional to angular acc.

Ir>Id>Is
therefore:
tr<td<ts

If anyone show where I went wrong, it'll be of great help.

2. Jul 12, 2015

### CWatters

Can you explain? The moment of inertia of an object is normally a constant that depends on the objects shape (among other things). For example if you spin up a flywheel it's moment of inertia doesn't change.

3. Jul 12, 2015

### Avaron Cooper

Since the radii of the objects are equal and their masses are equal, i took the torque acting on them to be equal.

4. Jul 12, 2015

### Avaron Cooper

therefore considering torque= I * Angular acc. , I took angular acc is indirectly proportional to I

5. Jul 12, 2015

### paisiello2

I think you meant to say "inversely proportional".

So if the accelerations are smaller for larger moments of inertia, what does that do to the time?

6. Jul 12, 2015

### Avaron Cooper

oh.. Stupid me.. Smaller accelerations means longer time.. Thank you very much!!

7. Jul 12, 2015

### CWatters

8. Jul 12, 2015

### paisiello2

9. Jul 12, 2015

### Avaron Cooper

Thank you very much!!