Final answer:
In football mechanics, the kicker's leg rotates about the hip joint, creating angular velocity and exerting a force on the ball. Angular velocity is calculated using the linear velocity of the shoe tip and the radius from the hip joint to the tip. Average force on the ball is determined by the change in momentum during the brief time the foot is in contact with the ball.
Step-by-step explanation:
The mechanics of kicking a football involve a combination of physics concepts, including rotational motion and energy. When a kicker punts a football, their leg acts as a lever rotating about the hip joint, with the moment of inertia and the angular velocity determining the rotational kinetic energy of the leg.
Part A: Angular Velocity
To find the angular velocity of the shoe tip, we use the formula ω = v / r, where ω is the angular velocity, v is the linear velocity, and r is the radius (distance from the hip joint to the tip of the shoe). Given a linear velocity of 35.0 m/s and a radius of 1.05 m, the angular velocity is ω = 35.0 m/s ÷ 1.05 m = approximately 33.3 rad/s.
Part B: Average Force on Football
The average force exerted on the football during the kick can be calculated using the change in momentum over time. The formula is F = Δp / Δt, where Δp is the change in momentum (m×v) and Δt is the time duration of the force applied. With the football mass (0.500 kg), final velocity (20.0 m/s), and contact time (20.0 ms), we can find the average force.
Part C: Velocity Greater Than Shoe Tip
A football can achieve a velocity greater than the shoe tip's velocity because of the lever effect and the additional force applied by the foot during contact. The foot accelerates the ball beyond the initial speed at the point of contact due to the transfer of kinetic energy and the impulse applied.