b) On an old-fashioned rotating piano stool, a woman sits holding a pair of dumbbells at a distance of 0.60 m from the axis of rotation of the stool. She is given an angular velocity of 3.00 rad/s, after which she pulls the dumbbells in until they are only 0.20 m distant from the axis. The woman's moment of inertia about the axis of rotation is 5.00 kg m² and may be considered constant. Each dumbbell has a mass of 5.00 kg and may be considered a point mass. Ignore friction. (a) What is the initial angular momentum of the system? (b) What is the angular velocity of the system after the dumbbells are pulled in toward the axis? (c) Compute the kinetic energy of the system before and after the dumbbells are pulled in. Account for the difference, if any

A car initially traveling at 24.2 m/s undergoes a constant negative acceleration of magnitude 1.70 m/s2 after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.345 m? rev(b) What is the angular speed of the wheels when the car has traveled half the total distance?

A car initially traveling at 27.2 m/s undergoes a constant negative acceleration of magnitude 1.80 m/s2 after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.335 m? ?rev(b) What is the angular speed of the wheels when the car has traveled half the total distance?? rad/s

Two astronauts (figure), each having a mass of 76.0 kg, are connected by a d = 11.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.50 m/s. CM d (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum of the two-astronaut system. |kg · m²/s (b) Calculate the rotational energy of the system. kJ (c) By pulling on the rope, one astronaut shortens the distance between them to 5.00 m. What is the new angular momentum of the system? |kg · m²/s (d) What are the astronauts' new speeds? m/s (e) What is the new rotational energy of the system? kJ (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? kJ Need Help? Read It Master It

A student sits on a rotating stool holding two 4.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg-m? and is assumed to be constant. The student then pulls the objects horizontally to 0.20 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student system before and after the objects are pulled in. before after

Just after a motorcycle rides off the end of a ramp and launches into the air, its engine is turning counterclockwise at 7800 rev/min. The motorcycle rider forgets to throttle back, so the engine's angular speed increases to 13000 rev/min. As a result, the rest of the motorcycle (including the rider) begins to rotate clockwise about the engine at 3.10 rev/min. Calculate the ratio IE/IM of the moment of inertia of the engine to the moment of inertia of the rest of the motorcycle (and the rider). Ignore torques due to gravity and air resistance.

A 170-kg merry-go-round of radius 2.10 m is rotated by pulling a rope that is wrapped around its edge. What is the magnitude of the force (assume it to be constant) on the rope needed to bring the merry- go-round from rest to an angular speed of 0.400 rev/s in 3.00 s? (The moment of inertia of merry-go- round is 1/2MR2).

A 0.45 kg tetherball is attached to a pole and rotating in a horizontal circle of radius r₁ = 1.4 m and is circling at angular speed = 1.42 rad/s. As the rope wraps around the pole the radius of the circle shortens and became r2 = 0.9 m, that decreases the moment of inertia of the rotating tetherball. Neglecting air resistance what will be the angular speed of the ball after the rope is wrapped around the pole measured in kgm2/s (answer with 3 decimal places)? A