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A CD player rotates a compact disk about its central axis with constant angular acceleration. Starting from rest at t = 0 s, the CD completes 5 revolutions in 5 seconds. The rotational kinetic energy of the disk at t = 5 s is 25 J. Calculate the moment of inertia with respect to the disk's central axis.
You wish to study how the moment of inertia of an object affects its kinetic energy. To do that, you use a 1/8-scale model bicycle wheel, rotating at a constant angular speed and having a rotational kinetic energy of 48 J. You are told that the radius of the full-scale bicycle wheel is multiplied by the scaling factor f and its mass by f 3. What will be the rotational kinetic energy of the full-scale bicycle wheel made of the same substance and rotating at the same angular speed as the 1/8-scale model?
The flywheel of a steam engine rotates at an angular speed of 70 rad/s. When it releases 80J of kinetic energy, its angular speed drops to 40 rad/s. What is the needed moment of inertia?
A 500 g solid cylinder with a diameter of 12.0 cm is rolled down from rest on an inclined plane which is 1.5 m long and making an angle of 30 degrees with the horizontal. It reaches the bottom of the slope without slipping. Determine the ratio of its rotational kinetic energy to total kinetic energy.
Calculate the energy linked with a tornado, hypothetically represented as a uniformly rotating cylindrical mass of air (density: 1.2 kg/m³) with a radius of 55 m and a height of 2.0 km. Consider the wind velocity is 300 km/h in the most intense zone which is at the outer edge of the cylinder.
Calculate the kinetic energy of a planet revolving around the Sun. Assume the planet is spherical with a mass of 7.0×1024 kg and is located at a distance of 2.0×108 km from the Sun. The planet takes 1 year to revolve once around the Sun and the radius of the planet is 5.8×106 km.
An electric skateboard, including its battery pack, has a total mass of 15.0 kg. It is equipped with four small wheels, each with a mass of 0.30 kg and a diameter of 0.10 m. If the electric motor applies a force of 50.0 N to propel the skateboard forward, calculate its acceleration if it is initially at rest. Assume that the wheels can be modeled as solid cylinders and that there are no frictional losses.