An 85.0 kg baseball player who has leapt vertically into the air to catch a line

Question

An 85.0 kg baseball player who has leapt vertically into the air to catch a line drive catches the ball as it is headed horizontally directly into his glove. The ball has a mass of 145 g and is headed perpendicular to his arm at 52.0 m/s just before he catches it.
Just after he catches the ball with his arm extended horizontally, what is the player's angular speed about a vertical axis through his head and feet, assuming that he was stationary at the instant he caught it? To make the calculations reasonable, you can model the player's body as a uniform solid cylinder of mass 73.0 kg and diameter 35.0 cm and his arms as thin 6.00 kg rods, each 70.0 cm long, pivoting around a vertical axis through his center.

Explanation / Answer

wearegiven with massof the body mb = 73 kg radiusof the body rb = 35 cm / 2 =17.5 cm =0.175 m mometof inertia I = (1 / 2) mb rb2 = ........ kg . m2 mass ofthe arm ma = 6 kg lengthof the arm L = 70 cm = 0.70 m as thearm is taken as the rod its moment of inertia is = (1 / 3)ma L2 themoment of inertia of each arm is Ta = (1 / 3) (6 kg) (0.70m)2 = .......... kg . m2 so thetotal moment of inertia of the base ball will be I= Ib + 2 Ia = .......... kg . m2 let? is the angular speed of the player after he caught theball thenangular momentum is I ? nowball comes to rest after catching the ball, therefore its angularmomentum is zero angularmomentum of the player and ball after catching the ballis I? + 0 = I ? nowbefore catching the ball , ball is moving with a speed 52m / sperpendicular to the hand of player ballis moving at a perpendicular distance of r = 70 cm from the axispassing through his headand feet massof ball mball = 145 g = 0.145 kg angularmomentum of ball before it is caught by the player ismball v r angularmomentum of player and ball before catching the ball is = (0.145kg) (52 m / s) (0.70 m) =.......... kg / m2 Fromconservation of angular momentum we get I? = = .......... kg / m2 ?= ......... rad / s

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