A merry - go- round with a mass of 300 kg is spinning about an axis through its center with an angular speed of 5.2 2rad / s . A 45 kg child hops straight downward onto the outer edge of the merry -go -round . What is the rotational speed in rotations per minute ( rpm) of the merry -go round , once the child hops on Treat the merry go round as a solid disc and treat the child as a point mass.

A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 2 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 120 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)?   Please write out steps, not type-I have dyslexia

A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 4 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 80 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)?

A cockroach of mass m lies on the rim of a uniform disk of mass 3.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.434 rad/s. Then the cockroach walks halfway to the center of the disk.(a) What then is the angular velocity of the cockroach-disk system?(b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?

A sanding disk with rotational inertia 0.0012 kg-m2 is attached to an electric drill whose  motor delivers a torque of magnitude 15 N-m about the central axis of the disk.  About that axis and with a torque applied for 48 millisecond, what is the magnitude of the angular momentum?

Suppose a 0.230 kg ball is thrown at 18.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in the figure below. V (a) Calculate the final linear velocity (in m/s) of the person, given his mass is 92.0 kg. m/s (b) What is his angular velocity (in rad/s) if each arm is 8.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.810 m) and the rest of his body as a uniform cylinder of radius 0.170 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center. rad/s (c) Compare the initial and final total kinetic energies. O Initial kinetic energy is the same as final kinetic energy. O Initial kinetic energy is less than final kinetic energy. O Initial kinetic energy is greater than final kinetic energy.

A uniform thin rod of length 0.70 m and mass 5.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is a rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of the bullet velocity makes an angle of 60° with the rod (see the figure). If the bullet lodges in the rod and the angular velocity of the rod is 11.0 rad/s immediately after the collision, what is the magnitude of the bullet's velocity just before impact?

A cockroach of mass m lies on the rim of a uniform disk of mass 6.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.502 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? (b) What is the ratio K/Ko of the new kinetic energy of the system to its initial kinetic energy? (a) w = i (b) K/Ko =

(a) What is the final velocity, in m/s, of a hoop that rolls without slipping down a 7.10 m high hill, starting from rest? m/s (b) What would be the final velocity, in m/s, if a disk of the same mass and radius as the hoop rolled down the hill? m/s