Final answer:
When kicking a football, the rotation of the leg about the hip joint is a concept in physics involving angular motion. The angular velocity and average force during a kick can be calculated using physics equations related to rotational motion and the impulse-momentum theorem. The correct option stating that the kicker rotates their leg about the hip joint is A. True.
Step-by-step explanation:
When a football kicker rotates their leg about the hip joint, it is an example of angular motion in physics. To answer the questions posed:
(a) To find the angular velocity of the shoe tip we can use the relationship between linear velocity (v) and angular velocity (ω), which is v = rω, where r is the radius or the distance from the hip joint to the tip of the shoe. Given v = 35.0 m/s and r = 1.05 m, we solve for ω to get ω = v/r, so ω = 35.0 m/s / 1.05 m which equals approximately 33.33 radians per second.
(b) The average force exerted on the football can be found using the impulse-momentum theorem. Impulse equals the change in momentum, or force × time equals mass × change in velocity. Given that the force acts for 20.0 ms (0.020 s) to change the football's velocity from 0 to 20.0 m/s, and the mass of the football is 0.500 kg, we can find the average force F as follows: F × 0.020 s = 0.500 kg × 20.0 m/s, thus F = (0.500 kg × 20 m/s) / 0.020 s which equals 500 N.
The rotational kinetic energy of the leg is related to both the moment of inertia and the angular velocity. Using the rotational kinetic energy equation KE = (1/2)Iω², and given that I = 3.75 kg·m² and KE = 175 J, we can solve for ω using ω = sqrt((2 × KE) / I), and subsequently find the tip velocity with v = rω. In the final part, the correct option concerning the initial statement about the kicker rotating his leg about the hip joint is A. True.