Question

1. During the game against the Philadelphia Eagles last Sunday Eli Manning threw a football in a tight spiral.
(a) If the ball spun at a rate of 550 rpm, what was its angular velocity in rad/s?
(b) If it spun for 1.5 seconds before it was caught by Odell Beckham Jr., how many radians did it rotate in total and how many revolutions did it rotate in total? Assume there was no air resistance.

2. Now let's consider a more realistic situation, in which there was air resistance. So, the ball slowed down and pun slower (300 rpm) when it was caught by Odell.
(a) What was the angular acceleration?
(b) In this case, how many revolution did the ball make?

3. Mariano Rivera, who is considered the best closer in the history of MLB, threw his last pitch (a 89 mph 2-seam fast ball) in his career to Yunel Escobar of Tampa Bay Rays, which Escobar popped up for an easy out. If the ball was spinning at 1,400 rpm when it left to the ball, and (b) compute the force Mariano applied to the ball's surface. The mass and radius of the baseball is 147 g and 3.7 cm.

Answer 1

(1)
(a)
Speed = 550 rpm
Converting to rad/s
Speed = (550 * 2π)/60
Speed = 57.6 rad/s

(b)
Total rotation in rad = 57.6 * 1.5 = 86.4 rad

No of rev per second = 550/60 = 9.166
No of rev in 1.5 s , = 9.166 * 1.5 = 13.75 revolution

(2)
(a)
wf = (300 * 2*π)/60
wf = 31.4 rad/s

wf = wi + α*t
31.4 = 57.6 - α*1.5
α = 17.5 rad/s^2
angular acceleration, α = 17.5 rad/s^2

(b)
wf^2 = wi^2 - 2*α*θ
31.4^2 = 57.6^2 - 2*17.5*θ
θ = 66.6 rad

1 rev = 2π rad
No of rev = 66.6/(2π)
No of rev = 10.6 revolution

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