At a particular instant, a 1.0 kg particle's position is r = (3.0î - 4.0j + 5.0k) m, its velocity is v = (-1.0î + 4.0j + 1.0k) m/s, and the force on it is F = (12.0î + 17.0j) N. (Express your answers in vector form.) (a) What is the angular momentum (in kg · m2/s) of the particle about the origin? kg - m?/s (b) What is the torque (in N • m) on the particle about the origin? T3D N.m (c) What is the time rate of change of the particle's angular momentum about the origin at this instant (in kg · m2/s?)? IP dt kg - m?/s2 %3D

Three children are riding on the edge of a merry-go-round that is 162 kg, has a 1.60 m radius, and is spinning at 15.3 rpm. The children have masses of 17.4, 29.5, and 40.8 kg. If the child who has a mass of 29.5 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

A merry-go-round at an amusement park consists of an outer ring of horses and an inner ring of elephants. The ring of eight horses has a radius of rh = 8.9 m. Each of the eight horses has a mass mh = 110 kg. The ring of four elephants has a radius of re = 6.5 m and each of the four elephants has a mass me = 195 kg. The platform of the merry-go-round itself has a mass of mp = 1500 kg and a radius of rp = 10.5 m. At it’s operating speed, the merry-go-round makes one revolution every t = 11 s.Enter an expression for the total moment of inertia of the carousel about its axis, in terms of the defined quantities. I =Calculate the moment of inertia of the carousel about its axis, in units of kilogram meters squared. I =Enter an expression for the angular speed of the carousel, in terms of the defined quantities. ω =  Calculate the carousel’s angular speed, in radians per second.  ω =

To study torque experimentally, you apply a force to a beam. One end of the beam is attached to a pivot that allows the beam to rotate freely. The pivot is taken as the origin or your coordinate system. You apply a force of F = Fx i + Fy j + Fz k at a point r = rx i + ry j + rz k on the beam. 1. Enter a vector expression for the resulting torque, in terms of the unit vectors i, j, k and the components of F and r.  2. Calculate the magnitude of the torque, in newton meters, when the components of the position and force vectors have the values rx = 3.03 m, ry = 0.035 m, rz = 0.085 m, Fx = 2.8 N, Fy = 4.8 N, Fz = 5.8 N.  3. If the moment of inertia of the beam with respect to the pivot is I = 71 kg˙m2, calculate the magnitude of the angular acceleration of the beam about the pivot, in radians per second squared.

The angular momentum of a sphere is given by , ?=(―4.59?^3)? + (6.01―1.19?^2)? + (6.26?)? where L has units of kg·m2/s when t is in seconds. What is the net torque on the sphere as a function of time?

In the figure here, a cylinder having a mass of 1.5 kg can rotate about its central axis through point O. Forces are applied as shown: F₁ = 3.1 N, F2 = 9.3 N, F3 = 6.0 N, and F4 = 9.1 N. Also, r = 7.0 cm and R = 17 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) Number FA Rotation axis F₁ Unit 7

During a trampoline routine, a gymnast is tumbling in the air at 21 rad/s in a tuck position. He then extends into a layout position and doubles his radius of gyration just before landing on the trampoline bed.   How fast is his angular velocity in rad/s at this instant, just before landing on the trampoline bed?

The angular speed of a rotating platform changes from ω0 = 3.6 rad/s to ω = 6.4 rad/s at a constant rate as the platform moves through an angle Δθ = 5.5 radians. The platform has a radius of R = 12 cm. Calculate the angular acceleration of the platform α in rad/s2.

Consider the two vectors A= 12i + 5j and B = -3i. What is the cross product Ax B? O51 k none of the answers -15k O 15 j 15 k O.51 k -21 O 21 k -51

In the figure here, a cylinder having a mass of 2.7 kg can rotate about its central axis through point O. Forces are applied as shown: F₁ = 8.0 N, F₂ = 9.6 N, F3 = 6.0 N, and F4 = 6.4 N. Also, r = 5.4 cm and R = 10 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) Number IN Unit Rotation axis F₁ R 0