13. Rotational Inertia & Energy

Intro to Rotational Kinetic Energy

13. Rotational Inertia & Energy

Intro to Rotational Kinetic Energy

Guided videos.

A flywheel is a rotating disc used to store energy. What is the maximum energy you can store on a flywheel built as a solid disc with mass 8 × 10⁴ kg and diameter 5.0 m, if it can spin at a max of 120 RPM?

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Multiple Choice

When solid sphere 4 m in diameter spins around its central axis at 120 RPM, it has 10,000 J in kinetic energy. Calculate the sphere's mass.

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Multiple Choice

What is the mass of a solid sphere with radius

5.0 cm

, that has

2.5 J

of kinetic energy when it rotates at

34 rad / s

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Textbook Question

A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t = 0, the wheel turns through 8.20 revolutions in 12.0 s. At t = 12.0 s the kinetic energy of the wheel is 36.0 J. For an axis through its center, what is the moment of inertia of the wheel?

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Textbook Question

An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod. (a) What is its rotational kinetic energy? (b) Suppose that, due to weight constraints, you had to reduce the propeller's mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?

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Textbook Question

If we multiply all the design dimensions of an object by a scaling factor f, its volume and mass will be multiplied by f^3. (b) If a 1/48 scale model has a rotational kinetic energy of 2.5 J, what will be the kinetic energy for the full-scale object of the same material rotating at the same angular velocity?

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Textbook Question

A uniform sphere with mass 28.0 kg and radius 0.380 m is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere. If the kinetic energy of the sphere is 236 J, what is the tangential velocity of a point on the rim of the sphere?

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Textbook Question

The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min. What moment of inertia is required?

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Textbook Question

A 140-g baseball, with a diameter of 7.5 cm, is pitched at 145 km/h. It spins at 1200 rpm. If the baseball is assumed to be a uniform solid sphere, what fraction of its kinetic energy is rotational?

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Textbook Question

An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25 incline. It rolls, without slipping, to the bottom(b). What fraction of its kinetic energy is rotational?

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Textbook Question

A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim?

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Textbook Question

What is the rotational kinetic energy of the earth? Assume the earth is a uniform sphere. Data for the earth can be found inside the back cover of the book.

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Textbook Question

A small 300 g ball and a small 600 g ball are connected by a 40-cm-long, 200 g rigid rod. b. What is the rotational kinetic energy if the structure rotates about its center of mass at 100 rpm?

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Textbook Question

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. Its maximum angular velocity is 1200 rpm. b. How much energy is stored in the flywheel?

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Textbook Question

(II) A merry-go-round has a mass of 1240 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.00 s? Assume it is a solid cylinder.

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Textbook Question

(II) Two ice skaters, both of mass 68 kg, approach on parallel paths 1.6 m apart. Both are moving at 3.5 m/s with their arms outstretched. They join hands as they pass, still maintaining their 1.6-m separation, and begin rotating about one another. Treat the skaters as particles with regard to their rotational inertia.

(b) Calculate the change in kinetic energy for this process.

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Textbook Question

(III) The 1100-kg mass of a car includes four tires, each of mass 35 kg (including wheels) and diameter 0.80 m. Assume each tire and wheel combination acts as a solid cylinder.

(c) If the car is initially at rest and is then pulled by a tow truck with a force of 1500 N, what is the acceleration of the car? Ignore frictional losses.

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13. Rotational Inertia & Energy

Intro to Rotational Kinetic Energy

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