Question

while punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.8 kg/m² and its rotational kinetic energy is 150 j. What is the angular velocity of the leg in rad/s and what is the velocity of the tip of the punter's shoe in m/s if it is 1.45 m from the hip bone?

Answer 1

The angular velocity of the kicker's leg is approximately 8.84 rad/s, and the tip of the shoe moves with a velocity of approximately 12.82 m/s, given the moment of inertia and the rotational kinetic energy provided.

Step-by-step explanation:

The question involves calculating the angular velocity of a kicker's leg and the velocity of the tip of the shoe during a football punt.

Finding the Angular Velocity

Using the relationship between rotational kinetic energy (KErot) and angular velocity (ω), we can write KErot = (1/2)Iω2. The moment of inertia (I) is given as 3.8 kg/m2, and the KErot is 150 J. Solving for ω:

150 J = (1/2)(3.8 kg/m2)ω2

ω2 = (2 × 150 J) / 3.8 kg/m2

ω2 = 300 J / 3.8 kg/m2

ω = √(300 J / 3.8 kg/m2)

ω ≈ 8.84 rad/s

Velocity of the Shoe Tip

Next, to find the velocity of the shoe tip (v), we use the relationship between angular velocity (ω) and linear velocity (v) at a radius (r), which is v = ωr. The distance from the hip joint to the tip of the shoe is 1.45 m:

v = 8.84 rad/s × 1.45 m

v ≈ 12.82 m/s

The angular velocity of the kicker's leg is approximately 8.84 rad/s and the velocity of the shoe tip is approximately 12.82 m/s.