A turntable with a mass of 12 kg and a radius of 2 meters spins at a constant angular velocity of 140 rpm. A 500-gram scoop of uniformly-dense ice cream falls onto the turntable, so the scoop's center of mass is one meter away from the turntable's center. The scoop forms a hemisphere and has a radius of 4 cm. If there's no friction between the brick and ice cream scoop and they spin at the same angular speed, what is their final angular speed, in rev/min or in rad/s? Justify your answer with your rationale and equations used. Moments of Inertia: Idisk =MR? for rotation about its center of mass parallel to the z-axis. Inemisphere = MR for rotation about its center of mass parallel to the z-axis. Edit View Insert Format Tools Table

A figure skater with her arms outstretched has a moment of inertia of 4.08 kg-m2. When she brings her arms in to her chest, her moment of inertia drops to 2.53 kg-m2. If she spins at a rate of 64.2 rpm with her arms outstretched, calculate her new rotation rate (in rpm) when she brings her arms in.

A 3.0 kg particle moves in a circle of radius 2.0 m with an angular momentum of 30.0 kg⋅m2/s. What is its speed of rotation?

Three objects lie in the x, y plane. Each rotates about the z axis with an angular speed of 7.48 rad/s. The mass m of each object and its perpendicular distance r from the z axis are as follows: (1) m1 = 7.80 kg and r1 = 5.20 m, (2) m2 = 3.10 kg and r2 = 2.90 m, (3) m3 = 3.50 kg and r3 = 4.70 m. Find the tangential speed of (a) object 1, (b) object 2, and (c) object 3. (d) Determine the total kinetic energy of this system using the expression   (e) Find the rotational kinetic energy of the system using the relation  to verify that the answer is the same as that in (d).

A ride at a carnival has four spokes to which pods are attached that can hold two people. The spokes are each 15 m long and are attached to a central axis. Each spoke has mass 200.0 kg, and the pods each have mass 100.0 kg. If the ride spins at 0.2 rev/s with each pod containing two 50.0-kg children, what is the new spin rate if all the children jump off the ride?

Three children are riding on the edge of a merry-go-round that is a disk of mass 110 kg, radius 1.5 m, and is spinning at 18 rpm. The children have masses of 21.2 kg, 28.4 kg, and 33.8 kg.  If the child who has a mass of 28.4 kg moves to the center of the merry-go-round, what is the new magnitude of angular velocity in rpm?

Vlad needs to draw water from a deep well. He is using a bucket that is connected by rope (negligible mass) to a wooden axle at the top of the well. By cranking a handle at the end of the axle, Vlad is able to unwind the rope around the axle and move the bucket downward. The radius of the axle is R = 30 cm. The bucket is traveling downward at speed vi = 25 cm/s when the handle slips out of Vlad’s hand. As the rope unwinds and the bucket falls downward, the axle spins freely with an angular acceleration whose magnitude is α = 4.5 rad/s^2. The bucket falls through a distance of d = 7.0 m before crashing into the water. 1. What is the angular speed ωf of the axle when the bucket first hits the water?  2. As d → 0, what limit does ωf approach and why?

A lawnmower blade has a length of 0.75 m and a mass of 1.5 kg. The blade rotates around its center at an angular velocity of 500 re. The end of the blade hits a 0.25 kg croquet ball (point mass), and the ball sticks to the blade. min Before the collision, the ball was stationary. After the collision, the ball will be moving at the same angular velocity as the blade at a distance of half of the blade length from the axis of rotation. Treat the blade as a rod rotating around its center. The final angular velocity of the lawnmower blade and croquet ball combo is rad S

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. A star with a of mass of 2.0x1032 kg and radius 7.0x108 m is initially rotating at a rate of once every 30 days. The star collapses into a neutron star with the same mass but a new radius of 16,000 m. What is the angular speed of the star? (Give your answer in rotations per second.) Assume the star is a solid sphere: Isphere = 2/5 MR2.   The Crab Nebula (shown below) formed from a nearby supernova (6000 light years away). Chinese astronomers observed the event in the year 1054 and since that time the nebula has been expanding into what it appears like today. The Crab Pulsar is a neutron star at the center of the nebula and the remains of the original supernova.

What is the magnitude of the angular momentum of a 5.0 kg ball spinning at 15 rev/s?. The diameter of the ball is 24 centimeters.