Question

Four wheels of different radii are connected with pulleys as shown below. Wheels 2 and 3 have a common axle. If the angular velocity of Wheel 2 is 2 revolutions per second, what is the angular velocity of Wheel 4?

Answer 1

For,these set of wheels fixed to pulleys, with belts,velocity of centre of mass(`v_(cm)`) is constant,

We know, `v=omega*r` (where, `omega` is the angular velocity and `r` is the radius)

So,if `v_(cm)` is the same for wheel `2` and `3`

We,can say, `omega_2 * r_2 = omega _3 *r_3`

Given ,`omega_2 = 2, r_2 = 1, r_3 =4`

So, `omega_3 = 1/2`

Similarly, wheel `4` is rotating due to the motion of wheel `3`,

So,they will also have same `v_(cm)`

So,we can write, `omega_4 * r_4 = omega _3 *r_3`

Given, `r_4 = 2 , r_3 =4 ,omega _3 =1/2`

So, `omega _4 =1`

So,the wheel `4` will be rotating at `1` revolution per minute angular speed