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.
A wind turbine blade rotates at 10 revolutions per minute about its central axis. The length of the blade is 5 m and its mass is 20 kg. The blade can be considered like a thin rod. i) Determine the blade's rotational kinetic energy. ii) Due to practical constraints, it will be more convenient to divide the weight of the blade by 2. What would be the angular speed needed in order to maintain the same blade size and the same kinetic energy?
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 f3. 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?
A homogeneous metal sphere rotates about a frictionless axle at its center of mass at a constant angular velocity. The rotational kinetic energy of the sphere is 150J. What is the tangential velocity of a point on the rim of the sphere if the diameter of the sphere is 20 cm and its mass is 1.0 kg?
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?