In the figure here, a 25 kg child stands on the edge of a stationary merry-go-round of radius 1.6 m. The rotational inertia of the merry- go-round about its rotation axis is 140 kg-m2. The child catches a ball of mass 0.5 kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity of magnitude 10 m/s, at angle o = 26° with a line tangent to the outer edge of the merry-go-round, as shown. What is the angular speed of the merry-go-round just after the ball is caught? Ball Child W = i

A playground merry-go-round, with radius 2.9 m and moment of inertia 127 kg m2, rotates with an angular speed 2.7 rad/s. A boy (mass 46 kg), initially at rest, hops onto the outer edge of the merry-go round. What is the new angular speed (in rad/s) just after the boy has jumped on?

At the instant of the figure, a 8.90 kg particle P has a position vector of magnitude 6.60 m and angle 01 = 42.0° and a velocity vector of magnitude 7.90 m/s and angle 02 = 31.0°. Force 7, of magnitude 8.70 N and angle 03 = 31.0° acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? (a) Number i (b) Number i V 0₂ Units Units F03/ -X ◄► ◄►

In the figure here, a 29 kg child stands on the edge of a stationary merry-go-round of radius 2.2 m. The rotational inertia of the merry- go-round about its rotation axis is 100 kg⋅m². The child catches a ball of mass 0.9 kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity of magnitude 9 m/s, at angle = 38° with a line tangent to the outer edge of the merry-go-round, as shown. What is the angular speed of the merry-go-round just after the ball is caught? W = i Child Ball

A horizontal solid circular plate of mass 60 kg rotates about a vertical axis passing through its center at period of T = 6 s. A block of mass 60 kg is placed on the edge of the plate and rotating with the plate. Now, let’s move the block from the edge of the plate to the center of the plate. What is the velocity of rotation now? (Hint: You may consider angular momentum conservation.)

A massless, frictionless merry-go-round of radius R has one child of mass M sitting on the outer edge and is spinning with angular velocity ωi. If the child walks towards the center until she is 0.50R from the center, by what factor does the angular velocity increase? (i.e. solve for F where ωf=Fωi)

Modeled after the triatomic molecule problem that is let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 6.778 kg, with x coordinate at 2.814 m and y coordinate at 9.967 m. The second atom has a mass of 48.003 kg, with x coordinate at 47.145 m and y coordinate at 17.003 m. The third atom has a mass of 43.312 kg, with x coordinate at 44.89 m and y coordinate at 22.657 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?