Question

If an object is rolling without slipping, how does its linear speed compare to its rotational speed? If an object is rolling without slipping, how does its linear speed compare to its rotational speed? v = Rω v = ω/R They are unrelated. v = ω

Answer 1

Answer:

$v = r\omega$

Explanation:

If the object is rolling without slipping, every unit of rotated angle equals to a distance perimeter rotated.

Suppose the object complete 1 revolution within time t. The angular distance is 2π rad. Its angular velocity is 2π/t

The distance it covered is its circumference, which is 2πr, and so the speed is 2πr/t

So the linear speed compared to angular speed is

$\frac{v}{\omega} = \frac{2\pi r/t}{2\pi /t} = r$

$v = r\omega$