Read This: It is common for a pitcher to throw a fastball that has a linear velo

Question

Read This: It is common for a pitcher to throw a fastball that has a linear velocity of 100 mph and rotational velocity of 2000 revolutions per minute (rpm). A Major League baseball has a weight of five ounces and a circumference of nine inches. Be very careful with units in the following calculations! PL1. What is the translational kinetic energy of a baseball that is thrown at 100 miles per hour? Give your answer in joules. PL2. A baseball has a weight of five ounces and a circumference of 9 inches. Assuming it has a uniform density, what is the moment of inertia of a baseball? Give your answer in kgm2 PL3. What is the rotational kinetic energy of a baseball that is spinning at 2000 rpm? Give your answer in joules

Explanation / Answer

we know, 1 ounce = 0.0283 kg

m = 5 ounce

= 5*0.0283

= 0.1415 kg

v = 100 mph

= 100*1609/(60*60) m/s

= 44.7 m/s

w = 2000 rpm

= 2000*2*pi/60

= 209.4 rad/s

2*pi*r = 9*2.54 cm

r = 3.64 cm = 0.0364 m

PL1) KE_trnaslational = (1/2)*m*v^2

= (1/2)*0.1415*44.7^2

= 141.4 J

PL2) I = (2/5)*m*r^2

= (2/5)*0.1415*0.0364^2

= 7.5*10^-5 kg.m^2

PL3) KE_rotational = (1/2)*I*w^2

= (1/2)*7.5*10^-5*209.4^2

= 1.64 J

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