"in softball, the pitcher throws with the arm fully extended (straight at the elbow). in a fast pitch the ball leaves the hand with a speed of 139 km/hr. (assume that the pitching motion originates with the arm straight back and terminates with the arm straight down. do not ignore gravity.) (a) find the rotational kinetic energy (in j) of the pitcher's arm given its moment of inertia is 0.720 kg · m2 and the ball leaves the hand at a distance of 0.604 m from the pivot in the shoulder. (enter the rotational kinetic energy of the pitcher's arm just after the ball is released.)"(b) what force (in n) did the muscles exert to cause the arm to rotate if their effective perpendicular lever arm is 4.00 cm and the ball is 0.187 kg? (enter the magnitude.) xn

Explanation:

139 km /h = 38.61 m / s.

the rotational kinetic energy (in J) of the pitcher's arm

= (1/2) I ω²

Where I is moment of inertia of the arm and ω is its angular velocity

Given , I = 0.72 kg m²

ω = vR , v is linear velocity and R is length of arm ( given .604 m )

ω = 38.61  x .604 = 23.32 rad / s

(1/2) I ω²

= .5 x 0.72 x (23.32)²

= 195.77 J

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.