1) In softball, the pitcher throws underhand with the arm fullyextended (straight at the elbow). In a fast pitch the ball, of massm = 0.156 kg, leaves the hand at a speed of 139 km/h, when the armis pointed vertically downward.
A) Find the rotational kinetic energy, in joules, of thepitcher’s arm-ball system, given that the arm's moment of inertiais 0.725 kg⋅m2 and the ball leaves the hand at adistance of 0.625 m from the pivot.
B) What force, in newtons, do the muscles exert to cause the armto rotate, assuming the force is constant and its effectiveperpendicular lever arm is 3.2 cm? Assume also that the pitcher'sarm starts extended horizontally behind her at rest and the ball isreleased at the bottom of the swing, as described in part (a).Approximate the arm as a uniform rod.
2. Zorch, an archenemy of Superman, decides to slow Earth’srotation to once per 29.5 h by exerting a force parallel to theequator, opposing the rotation. He uses an old Saturn V rocket,stolen from NASA, which was originally used to send astronauts tothe Moon. This rocket can exert a thrust of F = 3.85 ×107 N.
A)  If the original angular velocity of Earth isω0 and Zorch is trying to get the Earth to anangular velocity of ω, how much time will it take him? UseM and R for the mass and radius of the Earth.
B)How long, in seconds, will it take him to do this? (Noticethat this period gives Superman time to devote to thwarting othervillains.)
