13. Rotational Inertia & Energy

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?

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.

Which of the following expressions correctly gives the rotational kinetic energy $K$ of a rotating wheel with moment of inertia $I$ and angular speed $\omega$?

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?

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=(\(\frac\)12)I\(\omega\)^2$, for the $l = 1$ level, what is the rotational period (the time for one rotation)?

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?

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?

(II) Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms, that due to its yearly revolution about the Sun. [Assume the Earth is a uniform sphere with mass = 6.0 x 10²⁴ kg, radius = 6.4 x 10⁶ m, and is 1.5 x 10⁸ km from the Sun.]

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.

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?

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?

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?

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. Calculate the change in kinetic energy for this process.

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.