Question

A black disk rotates with constant speed and a coin that is located on the edge of the disk moves with speed v. If on a white disk that also rotates with constant speed, we place the same coin on the edge, it is moving with speed 4v. Which disk has a larger radius?

Answer 1

The white disk has a larger radius.

We know that the speed of the coin v = rω where r = radius of the disk and ω = angular speed of the disk.

Now, since both disks rotate at constant speed, ω = constant.

So, v ∝ r

For the black disk, its radius is r, the coins speed is v.

For the white disk, let its radius be R, the coins rotates at a speed V = 4v

We know that v ∝ r.

Since the coin on the white disk has a greater speed, so its radius would be greater.

So, the white disk has a larger radius.

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