Question

List two ways you can increase the linear velocity of a point on a rotating body.

Which factors can you control?

Which one would have the biggest impact? Why?

Answer 1

The linear velocity of a point on a rotating body is given by v = rω, where 'ω' is the angular speed of the body and 'r' is the radial distance of the point from the axis of rotation.

a) So to increase the linear velocity we can either increase the radial distance or increase the angular speed of rotation.

b) If the point is fixed on the body, we cannot move it away from the axis of rotation. So radial distance is something we cannot control. But if we apply a torque on the body increasing it's angular speed, then the linear speed also will be increased. So the factor that we can control is the angular speed. For the torque we need to apply a force which will have a tangential component to the body about the rotational axis. So the force which is applied tangential to the body will have the biggest impact as it's full magnitude will contribute to the angular acceleration and it will have no other components in other directions.