A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 22.3 22.3 m/s at a distance of 0.480 0.480 m from the joint and the moment of inertia of the forearm is 0.550 0.550 kg·m2, what is the rotational kinetic energy of the forearm?

rotational kinetic energy of the forearm is 593.6Joules

Explanation:

Rotational kinetic energy is expressed as shown

(K.E)r = 1/2Iω²

I is the moment of inertia

ω is the angular velocity

Given I = 0.550kgm²

ω = v/r

v is the linear velocity of the ball relative to the elbow

r is the distance

ω = 22.3/0.48

ω = 46.46rad/s

Rotational kinetic energy = 1/2×0.55×46.46²

= 0.55×1079.27

= 593.6Joules

the total distance traveled by the car is

30km + 49km = 79 km .

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)