The rotational inertia of a collapsing spinning star changes to 1/4 its initial value. What is the ratio of the new rotational kinetic energy to the initial rotational kinetic energy? Number i Units

A uniform disk of mass 500 kg and radius 0.25 m is mounted on frictionless bearings so it can rotate freely around a vertical axis through its center (see the following figure). A cord is wrapped around the rim fo the disk and pulled with a force of 10 N. (a) How much work has the force done at the instant the disk has completed three revolutions, starting from rest? (b) Determine the torque due to the force, then calculate the work done by this torque at the instant the disk has completed three revolutions? (c) What is the angular velocity at the instant? (d) What is the power output of the force at that instant?

A uniform cylindrical grindstion has a mass of 10 kg and a radius of 12 cm. (a) What is the rotational kinetic energy of the grindstone when it is rotating at 1.5103rev/min ? (b) After the grindstone’s motor is turned off, a knife blade is pressed against the outer edge coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.

A pulsar is a rapidly rotating neutron star. The Crab nebula pulsar in the constellation Taurus has a period of 33.510-3s , radius 10.0 km, and mass 2.81030kg . The pulsar’s rotational period will increase over time due to the release of electromagnetic radiation, which doesn’t change its radius but reduces its rotational energy. (a) What is the angular momentum of the pulsar? (b) Suppose the angular velocity decreases at a rate of 1014rad/s2 . What is the torque on the pulsar?