A disk with a rotational inertia of 7.46 kg·m2 rotates like a merry-go-round while undergoing a torque given by τ = (5.54 + 7.56t) N · m. At time t = 1.00 s, its angular momentum is 8.05 kg·m2/s. What is its angular momentum at t = 3.00 s?

The figure above shows Einstein spinning on a platform. He is initially spinning at a rate of 1rev/s, and holding his hands a distance of R1 = 80.3 cm away from his body. He then pulls his arms in to a distance of R2 = 40cm, changing his rotational speed. In this problem you can model Einstein’s body as a cylinder with a moment of inertia I = 30MR2, where M is his mass (60kg), and R is the distance his hands are from his body. (Notice that the figure shows him holding weights, but we are going to assume they are massless, to make it simpler!)(a) If he draws his arms in very quickly, you can safely ignore any frictional force on the platform. Assuming this is true, how fast is he rotating after he draws his arms in? (b)  In reality, after he draws his arms in friction will start to slow him down. If this small amount of friction is applying a torque of 4 Nm to the platform, how long would it take before Einstein stops moving?

A typical helicopter with four blades rotates at 370 rpm and has a kinetic energy of 7.05 x 105 J. What is the total moment of inertia, in kg. m² of the blades?

A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 2.58 m and a rotational inertia of 255 kg·m2 about the axis of rotation. A 53.8 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.18 rad/s when the student starts at the rim, what is the angular speed when she is 1.79 m from the center?

A turntable s pins on a frictionless bearing. Its moment of inertia is 3.00 x 10-2 kg m2. It initially rotates at 25.0 rev/min about an axis through its center. Then, a 0.6-kg ball of putty is dropped vertically onto the turntable. It lands and sticks at a point 0.10 m from the center. By what factor does this collision change the angular momentum of the system? That is, Lafter = [factor] x Lpefore- (Hint: Since it moves vertically the putty has initial angular momentum of zero.) O a. 1.22 b.0.820 c. 1.00 (no change) d. 1.20

A turntable of radius R=2.00 m and mass M=32.0 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4x rad/s. The fixed turntable bearing is frictionless. The turn table is in the shape of a uniform disc with the moment of inertia of this turntable being I 0.5*MR?. (a) What is the magnitude of angular momentum of this turntable? Answer: 803.84 (b) What is the (magnitude of) the momentum of this turntable? Answer: 401.92 kgm2/s? X kgm/s? Now a lump of clay of mass m=2.48 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to a point 1.90 m from the axis (c) Find the final angular speed of the clay and turntable. Answer: 12.386 X rad/s

A 3.8-mm-diameter merry-go-round is rotating freely with an angular velocity of 0.80 rad/s. Its total moment of inertia is 1300 kg⋅m2. Four people standing on the ground, each of mass 61 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now? What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?

A solid disk rotates in the horizontal plane at an angular velocity of 4.50 x 10-2 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.13 kg.m?. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?

A carousel has a radius of 1.60 m and a moment of inertia of 130 kg · m2.A girl of mass 43.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.10 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.4 rad/s. How far from the center, in meters, did the girl stop?