Question

A wheel on a car is rolling without slipping along level ground. The speed of the car is 36 m/s. The wheel has an outer diameter of 50 cm. The speed of the top of the wheel is

Answer 1

The speed of the top of the wheel is twice the speed of the car.

That is: 72 m/s

Step-by-step explanation:

To find the speed of the top of the wheel, we need to combine to velocities: the tangential velocity of the rotating wheel due to rotational motion
`(v_t=\omega\,R=\omega\,(0.25\,m)\,)` - with
`\omega` being the wheel's angular velocity,

plus the velocity due to the translation of the center of mass (v = 36 m/s).

The wheel's angular velocity (in radians per second) can be obtained using the tangential velocity for the pure rotational motion and it equals:
`\omega=(v_t)/(r) =(36)/(0.25) \,s^(-1)`

Then the addition of these two velocities equals:

`\omega\,R+v=(36)/(0.25) (0.25)\,\,(m)/(s) +36\,\,(m)/(s) =72\,\,(m)/(s)`