Question

You catch a fastball with your hand and it applies a torque on your relaxed arm (you allow the ball to rotate your arm freely). you are given the mass of the ball m , the mass of your arm m , and the length of your arm r . what is the moment of inertia of the system?

a)mr²
b)mr²+(m+mₐᵣₘ)r²
c)mvr²
mr²/12

Answer 1

The moment of inertia of the arm and baseball system is the sum of the individual moments of inertia of the arm and the ball, which can be expressed as I = m_arm*r^2 + m_ball*r^2, where m_arm is the mass of the arm, m_ball is the mass of the baseball, and r is the length of the arm.

Step-by-step explanation:

The question asks for the moment of inertia of your arm and the baseball when you catch a fastball and it applies a torque on your relaxed arm. The moment of inertia (I) of the system (arm plus ball) would be the sum of the moment of inertia of the arm and the ball, since the ball and your arm both contribute to the overall inertia of the system. Considering the arm to be a solid object and the baseball a point mass, the moment of inertia is calculated by I = mar2 + mbr2, where ma is the mass of your arm, mb is the mass of the baseball, and r is the length of your arm from the pivot point (shoulder) to the place where you catch the ball (typically considered to be at the end of the fingertips).