Rotational Motion: conservation of angular momentum, energy.

Two astronauts (Fig.), each having a mass of 70.0 kg, are connected by a 11.0 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.70 m/s.

Two astronauts (Fig.), each having a mass of 70.0 kg, are connected by a 11.0 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.70 m/s.

(a) Treating the astronauts as particles, calculate the magnitude of the angular momentum.
kg · m2/s
(b) Calculate the rotational energy of the system.
J
(c) By pulling on the rope, one of the astronauts shortens the distance between ...

Solution Summary

Two astronauts connected by string orbiting each other in free space. The five parter related to angular momentum and energy is solved.

The time dependent position of three particles with masses m1=1kg m2=2kg and m3=3kg are:
r1 = (3+2t^2)i + 4j
r2 = (-2+1/t)i +2tj
r3 = i-3t^j
Find the total kinetic energy of the system
The rotational kinetic energy
The total angular momentum
The angular momentum of spin
The total torque

A 62.99 kg woman stands at the rim of a horizontal turntable having a moment of inertia of 495 kg·m^2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) a

Two lightweight rods L = 19.6cm in length are mounted perpendicular to a vertical axle and at 180 degrees to each other (see figure attached).
At the end of each rod is a m = 640 g mass. The rods are spaced h = 39.6cm apart along the axle. The axle rotates at 28.0rad/s such that the angular velocity vector points upward (+). W

See attached file for proper format.
A and B are two separate clutch plates. Plate A has a mass of 36 kg, a
radius of gyration of 0.12 m and rotates at 660 rev min-1. Plate B has a
mass of 45 kg, a radius of gyration of 0.16 m and is stationary.
When the clutch plates are engaged, slipping ceases after 0.4 seconds and
t

A neutron star has an angular spped of 70.4 rad/s and underwent a "glitch" that increased its angular speed to Ω= Ω0+ Δ;Ω where ΔΩ/Ω0 = 2.01 x 10^-6. If the radius of the neutron star before the glitch was 11 km, by how much did its radius decrease in the glitch - the neutron is a uniform sphere.
So far uniform sphere

A turntable has rotational inertia 0.021 kg-m^2 and is rotating at 0.29 rad/s about a friction-less vertical axis. A wad of clay is tossed onto the turntable and sticks 15cm from the rotation axis. The clay hits with horizontal velocity component 1.3 m/s, at right angles to the turntable's radius, and in a direction that opposes

A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of .667 rev/s. A 59.4 kg person running tangential to the rim of the merry-go-round at 3.38 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-ro

Mass m whirls on a frictionless table, held to circular motion by a string which passes through a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from L1 to L2.
Show that the work done in pulling the string equals the increase in kinetic energy of the mass.

Three disks are spinning independently on the same axle without friction. Their respective rotational inertias and angular speeds are I, w (clockwise); 2I, 3w (counterclockwise); and 4I, w/2 (clockwise). The disks then slide together and stick together, forming one piece with a single angular velocity. What will be the directio