Question

While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75 kg⋅m² and its rotational kinetic energy is 175 J.
(a) What is the angular velocity of the leg?
(b) What is the velocity of the tip of the punter's shoe if it is 1.05 m from the hip joint?

Answer 1

Answer:

9.6609 rad/s

10.143945 m/s

Explanation:

I = Moment of inertia = 3.75 kgm²

K = Kinetic energy = 175 J

r = Radius = 1.05 m

Kinetic energy is given by

$K=\dfrac{1}{2}I\omega^2\\\Rightarrow \omega=\sqrt{\dfrac{2K}{I}}\\\Rightarrow \omega=\sqrt{\dfrac{2\times 175}{3.75}}\\\Rightarrow \omega=9.6609\ rad/s$

The angular velocity of the leg is 9.6609 rad/s

Velocity is given by

$v=r\omega\\\Rightarrow v=1.05\times 9.6609\\\Rightarrow v=10.143945\ m/s$

The velocity of the tip of the punters shoe is 10.143945 m/s