6.3.1 The Kinetic Energy of Rotation

Question 1

The Kinetic Energy of Rotation

Answer 1

• To consider objects as concentrated at their center of mass is inaccurate if you are interested in calculating their energy states, particularly their kinetic energy. All rotating objects have kinetic energy due to their rotation.
• The kinetic energy of a rotating object of arbitrary shape is given by , where is the moment of inertia or moment of rotational inertia.
• The moment of inertia of a rotating object depends on how its mass is distributed around its rotational axis.

Question 2

The Earth has a mass of 5.98 × 10^24 kg, an average radius of 6.38 × 10^6 m, and makes one complete rotation in about 24.0 h (hours). Which of the following is the rotational kinetic energy of the Earth? (Assume the Earth’s moment of inertia to be 2.44 × 10^38 kg • m^2 ).

Answer 2

6.45 × 10^29 J

Question 3

True or false?
A twirling figure skater increases speed when her arms are drawn in and slows down as her arms are outstretched. In terms of the moment of inertia, this occurs because as the radius (over which the system mass is distributed) decreases, the rotational speed must compensate by increasing a proportional value.

Answer 3

true

Question 4

A microwave oven turntable with a 35.0 cm diameter makes one complete rotation in 0.849 s. A french fry riding at the outermost circumference of the turntable has a mass of 0.00700 kg. Which of the following is the french fry’s rotational kinetic energy?

Answer 4

5.87 × 10^−3 J

Question 5

The ball inside a personal computer mouse has a mass of 0.0270 kg and a diameter of 0.0218 m. If the mouse is moved a distance of 0.150 m in 0.329 s, which of the following is the mouse ball’s rotational kinetic energy during the movement? Assume the ball travels at a constant speed.

Answer 5

2.80 × 10^−3 J

Question 6

Tetherball is a game in which two players hit a ball, in opposing directions, that is tied by a rope to a central post. Each player tries to wind the rope around the post in one direction until the ball touches the post itself. The player that does this wins the game. The rope is 2.0 m long and the ball weighs 250 g. The starting player in a particular game holds the ball and hits it with her hand transferring 200 J of energy to the ball. What will be the angular velocity of the ball as it leaves her hand?

Answer 6

20 rad / s

Question 7

A bicycle wheel with a moment of inertia I = 0.60 kg • m2 is spinning at 5.0 revolutions per second. How much energy was required to set this wheel in motion?

Answer 7

296.1 J

Question 8

A toy yo-yo with a mass of about 65.0 g is suspended in “sleeping” position while spinning at approximately 275 rad / s. When the toy “wakes up,” it immediately winds up the string it is suspended by, appearing to climb a distance of 0.895 m. Which of the following is the yo-yo’s moment of inertia?

Answer 8

1.51 × 10^−5 kg • m^2

Question 9

A bicycle wheel with a moment of inertia I = 0.60 kg • m2, spinning with an angular speed of 30 rad / s, is slowed when you place your hand on the tire for 2 seconds. The angular speed when you remove your hand from the tire is 5 rad / s. The average power associated with the force of friction against your hand is −262.5 W.

Answer 9

false

Question 10

A given compact disc is known to have 0.0359 J of rotational kinetic energy when spinning at 50.0 rad / s. Which of the following is the rotational kinetic energy if the CD is spinning at 400 rad / s?

Answer 10

2.30 J