Four identical particle of mass 0.5 kg each are placed at the vertices of a 2 m x 2m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia (in kg · m²) of this rigid body about an axis that a. passes through the midpoints of opposite sides and lies in the plane of the square, 4 ☑ b. passes through the midpoint of one of the sides and is perpendicular to the plane of the square, 6 c. lies in the plane of the square and passes through two diagonally opposite particles? 4

A 3.00 kg solid sphere with a radius of 15 cm is rolling without slipping along a horizontal floor. The magnitude of the velocity of the center of mass is 3.00 m/s. What is the ratio of the sphere's rotational kinetic energy to its translational kinetic energy, KErot / KEtrans? 2.

A playground merry-go-round of radius R = 1.20 m has a moment of inertia I = 255 kg · m2 and is rotating at 9.0 rev/min about a frictionless vertical axle. Facing the axle, a 23.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round? rev/min Need Help? Read It Watch It

A 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as it rotates. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.

Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.70 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.   final angular velocity:   rpm

A playground uniform merry-go-round has a mass of 110 kg and a radius of 1.90 m and it is rotating at a rate of 40 revolutions per minute. a) What is its angular velocity [ in rad/s] after a 20-kg child gets onto it by grabbing its outer edge? The child is initially standing on the ground. b) What is the new angular velocity [in rad/s] after the child moves to the center of the merry-go-round?

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.