Question

While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.64 kg · m2 and its rotational kinetic energy is 162 J.(a) What is the angular velocity of the leg? (b) What is the velocity of tip of the punter's shoe if it is 1.05 m from the hip joint?

Answer 1

a) w = 9.4345 rad/s

b) V = 9.9062 m/s

Step-by-step explanation:

a)

we know that:

K =
`(1)/(2)IW^2`

where K is rotational kinetic energy, I is the moment of inerta and W is the angular velocity. So, replacing the values, we get:

162J =
`(1)/(2)(3.64)W^2`

solving for W:

w = 9.4345 rad/s

b) V = WD

where V is the velocity of the tip of the punter's shoe, W the angular velocity and D the distance between his hip joint and the tip of the punter's shoe. Replacing the values, we get:

V = (9.4345 rad/s)(1.05 m)

V = 9.9062 m/s