A 0.8 kg particle is traveling in the xy-plane along the line  y = 2.6 m with a velocity 4.1 m/s. What is the angular momentum (in kg · m2/s) of the particle about the origin? (Express your answer in vector form.)

A bicycle is traveling north at 6.84 m/s. The mass of the wheel, 2.6 kg, is uniformly distributed along the rim(I=mr2), which has a radius of 17.89 cm. What are the magnitude(in kg m2/s) and direction of the angular momentum of the wheel about its axle?

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 ◄► ◄►

A particle P with mass 8 kg has position vector r (r = 3.0 m) and velocity v (v = 30.0 m/s) as shown in the figure. It is acted on by force F (F = 4.0 N). All three vectors lie in the xy plane. About the origin, what is the z-component of the angular momentum of the particle? About the origin, what is the z-component of the torque acting on the particle?

A bird flies overhead from where you stand at an altitude of 310.0ĵ m and at a velocity horizontal to the ground of 14.0î m/s. The bird has a mass of 1.8 kg. The radius vector to the bird makes an angle ? with respect to the ground. The radius vector to the bird lies in the xy-plane. What is the bird's angular momentum (in kg · m2/s) about the point where you are standing? (Express your answer in vector form.)

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 person of mass m = 75 kg stands in the center of a large rotating disk with radius R = 5.0 m and total mass M. The rotates without friction and without any external torque, initially at an angular velocity of w. The moment of inertia of a disk is MR. Assume that the person can be approximated as point-like, i.e. the angular momentum is r x p. The person then walks radially outward. (a) What is the angular momentum of the system (person + disk) as a function of the person's radius, r, from the center? Write it in terms of m, M, R, and w. (b) If the disk is initially rotating at wo and it slows to wp =0.8 rad/s when the person is at the very edge, what is the mass of the disk? 1.1 rad/s when the person is in the exact center, (c) What is the rotational kinetic energy of the system before and after the person walks to the edge?

Physics written by hand.