# Rolling Motion of Ring, Disk, Sphere: tr<td<ts

• Avaron Cooper
In summary, the given objects (a ring, a disk, and a sphere) with the same mass and radius roll down an inclined plane without slipping. The moments of inertia for each object, Ir, Id, and Is, are inversely proportional to their angular accelerations and therefore, tr<td<ts. This means that the time taken for the ring, disk, and sphere to reach the bottom of the plane are in the order of tr, td, and ts respectively.
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

## Homework Equations

. torque=moment of inertia*angular acceleration

## 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.

Avaron Cooper said:
I took the torque acting on the objects to be the same theefore moment of inertia to be indirectly proportional to angular acc.

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.

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

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

Avaron Cooper said:
I took the torque acting on the objects to be the same theefore moment of inertia to be indirectly proportional to angular acc.
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?

Avaron Cooper
paisiello2 said:
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?
oh.. Stupid me.. Smaller accelerations means longer time.. Thank you very much!

Avaron Cooper
paisiello2 said:

Thank you very much!

## 1. What is rolling motion?

Rolling motion is a type of motion where an object moves forward while also rotating around its central axis.

## 2. How does rolling motion differ from sliding motion?

Rolling motion involves both translational and rotational motion, while sliding motion only involves translational motion.

## 3. What is the difference between a ring, disk, and sphere in terms of rolling motion?

A ring, disk, and sphere all have different moments of inertia, which affect their ability to roll. A ring has a higher moment of inertia and therefore has difficulty rolling, while a sphere has a lower moment of inertia and can roll more easily.

## 4. What factors affect the speed of rolling motion?

The speed of rolling motion is affected by the object's moment of inertia, the applied force, and the surface it is rolling on.

## 5. Can an object experience both rolling and sliding motion at the same time?

Yes, an object can experience both rolling and sliding motion at the same time if the applied force is not enough to overcome the friction between the object and the surface it is rolling on.

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