Three objects are spinning as shown in the figure. Each object has a total mass of m and a radius of R. The object on the left is a hoop with its mass evenly distributed around the rim. The object in the middle is a solid sphere with its mass evenly distributed throughout. The object on the right consists of a massless rod 2R long with a point mass of 0.5m attached to each end. Which object has the greatest moment of inertia and which one the least? Mass m Mass = m Mass = 0.5m The rod + masses is the largest; the hoop is the smallest The sphere is the largest, the hoop is the smallest The hoop is the largest; the rod + masses is the smallest The hoop is the largest; the sphere is the smallest The rod + masses is the largest; the sphere is the smallest

A bicycle wheel with a radius of 350 mm and a mass of (2.40x10^0) kg is spinning freely on a work stand at a rate of 2.0 rev/sec when a (1.0000x10^0) kg kitten jumps on it radially, holds on and starts spinning around. What is the new rotational velocity of the wheel in units of rev/s? Treat the wheel as a thin hoop. Give your answer with three significant figures.

A circular disk with a radius of 0.5 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.69 kg. The moment of inertia of a disc is I MR² = F₁ = 2.6 N applied at the outer edge of the disc. F₂ = 4 N applied at a distance of 0.26 from the center of the disc. What is the angular acceleration of the disc?

Phoebe has a new bicycle. As soon as she brings it home she goes for a test ride. In 4 minutes she covers a distance of 480.0 m. Find the angular velocity of the front wheel of the bicycle during this short trip. Assume that she rides at a constant speed and that the diameter of the front wheel is 24 inches.  (1 inch = 2.54cm)

Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 kg⋅ m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω1,z = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. The z component of their common angular velcoity is 8.837 rad/s How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. I get I need to use kinetic energy equations of 1/2*I*w2 but…

Consider the 13 kg motorcycle wheel shown in the figure. Assume it to be approximately a ring with an inner radius of 0.285 m and an outer radius of 0.325 m. The motorcycle is on its center stand, so that the wheel can spin freely. If the drive chain exerts a force of 2200 N at a radius of 4.95 cm, what is the angular acceleration of the wheel, in radians per square second?  What is the tangential acceleration, in meters per square second, of a point on the outer edge of the tire?   How long, in seconds, starting from rest, does it take to reach an angular velocity of 89.5 rad/s?

Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.40 m. The merry‑go‑round is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 280 N applied to its edge causes the wheel to have an angular acceleration of 0.946 rad/s2.    What is the moment of inertia of the wheel? What is the mass of the wheel? If the wheel starts from rest, what is its angular velocity after 5.40 s have elapsed, assuming the force is acting during that time?