In this worksheet, we will practice calculating the rotational kinetic energy of an object from its moment of inertia and other kinematic properties.

**Q2: **

A system consists of an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm mounted on a disk of mass 2.0 kg and radius 50 cm. The system rotates about an axis through the centers of the annular cylinder and of the disk at 10 rev/s.

What is the moment of inertia of the system?

What is the system’s rotational kinetic energy?

**Q3: **

The mass of a hoop of radius 3.00 m is 6.3 kg. The hoop rolls across a horizontal surface with a speed of 8.8 m/s.

What magnitude of work would be required to bring the hoop to rest?

The hoop starts to roll upward along a surface inclined at above the horizontal. How far along the incline will the hoop be displaced before coming instantaneously to rest?

**Q4: **

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
20.0 m/s at a distance of
0.480 m
from the joint and the moment of inertia of the forearm is
0.500 kg⋅m^{2},
what is the rotational kinetic energy of the forearm?

**Q5: **

A wheel of mass 32 kg has an angular velocity of . The wheel’s inner radius is 0.380 m and its outer radius 0.520 m. What is the wheel’s rotational kinetic energy?

- A J
- B J
- C J
- D J
- E J

**Q6: **

A diver goes into a somersault during a dive by
tucking in her limbs. Her rotational kinetic energy is 100 J and her moment of inertia with her limbs tucked in is 9 kg.m^{2}. What is her rate of rotation during the somersault?

- A
- B
- C
- D
- E

**Q7: **

An electric sander consists of a rotating disk of mass 0.30 kg and radius 30.0 cm. The disk rotates at 80 rev/s, but when applied to a rough wooden wall the rotation rate decreases by .

What is the rotational kinetic energy of the rotating disk when in contact with the wall?

How much does the disk’s rotational kinetic energy decrease when it is placed in contact with the wall?

**Q8: **

A system of point particles is rotating about a fixed axis at 4.0 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are kg and m, kg and m, and kg and m.

What is the moment of inertia of the system?

What is the rotational kinetic energy of the system?

**Q9: **

The mass of a hollow hoop of radius 1.0 m is 6.0 kg. It rolls across a horizontal surface with a speed of 10.0 m/s.

How much work is required to stop the hoop?

If the hoop starts up a surface at to the horizontal with a speed of 10.0 m/s, how far along the incline will it travel before stopping and rolling back down?

**Q10: **

The Earth has rotational kinetic energy due to the motion of the Earth’s mass about its own axis of rotation. The Earth also has kinetic energy due to the motion of its mass around the Sun. Use a value of kg for the mass of the Earth and a value of km for the radius of the Earth.

Calculate the kinetic energy of Earth due to its axial rotation.

- A J
- B J
- C J
- D J
- E J

Calculate the kinetic energy of the Earth due to its orbit around the Sun. Assume that the Earth moves around the Sun in a circular orbit of radius m.

- A J
- B J
- C J
- D J
- E J

**Q11: **

A small helicopter is propelled horizontally at a speed of 20.0 m/s by the rotation at 300 rpm of four rotor blades. Each blade is 50.0 kg in mass, 4.00 m in length, and can be modeled as a thin rod that is joined at one end to an axis of rotation that is perpendicular to its length. The mass of the helicopter including its rotor blades is kg.

Find the rotational kinetic energy of the blades.

- A J
- B J
- C J
- D J
- E J

Find the ratio of the rotational kinetic energy of the blades to the translational kinetic energy of the helicopter.

**Q12: **

A horizontal rod of length 0.500 m and negligible mass has six small washers hung from it, evenly spaced at apart, with a washer at each end of the rod, as shown in the diagram. Each washer has a mass of 20.0 g. The rod rotates uniformly at 5.00 rev/s about an axis at the midpoint of its horizontal length.