13. Rotational Inertia & Energy

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?

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?

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.

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?

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?

If we multiply all the design dimensions of an object by a scaling factor f, its volume and mass will be multiplied by f³. 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?

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?

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?

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?

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. What fraction of its kinetic energy is rotational?

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.

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?

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. How much energy is stored in the flywheel?

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. Determine the total kinetic energy of the car when traveling 95 km/h.