Question

The velocity that a motor moves at is related to the force that the motor can supply. While it is common to think that more force equals a larger velocity, motors typically run slower the more force they have to produce. For example, the muscles in our bodies are motors (they consume energy and do work). The force velocity relationship for our muscle is approximately F = F₀ – av, where F is the force that the muscle produces when it is moving at velocity v, and F₀ and a are constants. Suppose you want to hit a ball a far distance with a club. Is it better to swing the club fast or hard (i.e., by using a lot of force)? Explain. Is your answer consistent with common perception?

Answer 1

During rotational motion, insted of force ,torque which is responsible for rotation around an axis like motor, is defined as cross product of position vector and force vector.

                                                            

For rotation motion change of angular mometum with respect to time equal to applied torque. The magnitude of torque depends on three quantities: the force applied, the length of the arm and the angle between them. If lenght is large , applied force can be chosen small to get required torque to get rotational velocity. This imples that large rotation motion can be obtained by applying small force.

The force velocity relationship for our muscle is approximately F = F₀ – av

So it is not better to swing the club hard as distance is far . It is not consistent with common perception where velocity granted as a longitudinal only.