13. Rotational Inertia & Energy

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 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?

(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. Determine

(a) the total kinetic energy of the car when traveling 95 km/h .

(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. Determine

(b) the fraction of the kinetic energy in the tires and wheels.

(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.

(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.

(II) Hurricanes can involve winds in excess of 120km/h at the outer edge. Make a rough estimate of

(a) the energy, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 kg/m³) of radius 85 km and height 4.5 km.

(II) Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms, (a) that due to its daily rotation about its axis, [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.]

(II) Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms, (b) 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.]

(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.