Question

While punting a football, a kicker rotates their leg about the hip joint. The moment of inertia of the leg is 3.75 kg·m^2 and its rotational kinetic energy is 175 J.

What is the angular velocity of the leg?
a) 7.81 rad/s
b) 8.54 rad/s
c) 9.42 rad/s
d) 10.0 rad/s

Answer 1

The angular velocity of the leg is approximately 9.61 rad/s.

Step-by-step explanation:

The angular velocity of the leg can be calculated using the equation:

Rotational kinetic energy = (1/2) * moment of inertia * angular velocity^2

Substituting the given values:

175 J = (1/2) * 3.75 kg·m^2 * angular velocity^2

Simplifying the equation:

angular velocity^2 = 93.3 rad^2/s^2

Taking the square root of both sides:

angular velocity = 9.61 rad/s

Therefore, the angular velocity of the leg is approximately 9.61 rad/s.