1. A 0.295m diameter ball with an initial velocity of 6.256m/s rolls up a hill without slipping. Treating the ball as a spherical shell, calculate the vertical height it reaches.

2. A hallow ball of mass 0.367kg and radius 0.483m starts from rest at a height of 2m and rolls down a 30 slope. What is the linear speed of the ball when it leaves the incline?

3.A hallow ball of mass 0.493kgand radius 0.342m starts from rest at a height of 2m and rolls down a 30 slope. What is the angular speed of the ball when it leaves the incline?

4.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 24m/s at a distance of 0.37m from the joint and the moment of inertia of the forearm is 0.37kgm², what is the rotational kinetic energy of the forearm?

5.A hoop of radius 0.46m and mass 2.56kg rolls down a ramp of length 4.5m that makes an angle of 25 with the horizontal. The hoop starts from rest from the top of the ramp. Find the angular speed of the hoop at the bottom of the ramp.

6.A hoop of radius 0.44m and mass 3.91kg rolls down a ramp of length 4.5m that makes an angle of 25 with the horizontal. The hoop starts from rest from the top of the ramp. Find the linear speed of the hoop at the bottom of the ramp.

7. A solid ball of radius 0.28m and mass 4.69kg rolls down a ramp of length 4m that makes an angle of 12 with the horizontal. The ball starts from rest from the top of the ramp. Find the linear speed of the hoop at the bottom of the ramp.

8.A solid ball of radius 0.33m and mass 3.45kg rolls down a ramp of length 4m that makes an angle of 12 with the horizontal. The ball starts from rest from the top of the ramp. Find the angular speed of the hoop at the bottom of the ramp.

9.A runner taking part in the 200m dash must run around the end of a track that has a circular arc with a radius of curvature of 38m. If he complete the 200m dash in 2.2004s and runs at a constant speed throughout the race, what is the magnitude of centripetal acceleration as he runs the curved portion of the track?

10.Calculate the angular momentum of an ice skater spinning at 8.314rad/s given his moment of inertia is 10.213kg*m_².

11.Calculate the angular momentum of the Earth in its orbit around the Sun. Assume the Earth is a solid sphere with a mass of 6*10²⁴kg and a radius of 6400km. It takes 365 days to orbit the Sun. Your answer will be on the order of 10³¹. Enter the coefficient only.

12.Calculate the centripetal force on the end of a 101m (radius) wind turbine blade that is rotating at 0.63rev/s. Assume the mass is 4.695kg.

13.Calculate the moment of inertia of a skater given the following information: The 60kg skater is approximated as a cylinder that has a 0.111m radius.

14.Calculate the rotational kinetic energy in a motorcycle wheel if its angular velocity is 130rad/s. Assume mass is 14.14kg and radius is 0.375m.

15.What is the final linear velocity of a hoop that rolls without slipping down a 4.424m high hill, starting from rest?

16.While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 1.545kg *m² and its rotational kinetic energy is 200J. What is the angular velocity of the leg?

17.A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of 30rad/s² and her lower leg has a moment of inertia of 0.75kgm². What is the force exerted by the muscle if its effective perpendicular lever arm is 1.9cm?

18.Suppose you exert a force of 180N tangential to a 0.28m radius 75kg grindstone (a solid disk). What is the angular acceleration assuming negligible opposing friction?

19.

Suppose a 900kg car is an the bridge shown below with its center of mass haEfWEY between the hinges and the cable attachments. Find the force in F if the mass of the bridge is 2500kg