题目

英文
A 89 mph slider thrown by NY Mets Ace Matt Harvey spins at a rate of
1900 rpm.(a) What is the angular momentum of the slider?(b) If it takes 0.06 s for him
to spin the ball from rest when he pitches,what is the torque he applies to the ball?A
baseball is 0.14 kg in mass and 9.25 inches in circumference.

提问时间：2020-10-17

答案

Sol：
(a)n=1900rpm=95/3 r/s
ω=2πn=190π/3 rad/s
(b)As we know,the baseball maybe full of the wood or wool,so we can assume the baseball is a solid ball.
we will get the moment of inertia of the baseball should be:
I = ∫m/(4πR³/3)4πr²·r²dr
=(3m/R³)∫r^4dr
=(3/5)mR²
the circumference C=2πR=9.25 inches = 0.23495m
M=Iβ=I(ω-0)/t=(3/5)×0.14kg×(0.23495m)²×190π/3 /s÷0.06s=15.38N·m