A student sits on a frictionless, freely rotating stool that is initially at rest. The student holds two identical 1.0kg masses at arm’s length, each located 0.75m from the rotation axis. The combined moment of inertia of the student–stool system without the masses is Ibody=4.5kgm2.
The student simultaneously pulls the two masses straight inward to a distance of 0.30m while a friend standing nearby gently taps one mass tangentially, giving it an instantaneous speed of 3.0m/s relative to the student at the moment it reaches the inner position. Neglect external torques during this brief event.
(a) Calculate the angular momentum of the tapped mass about the rotation axis immediately after the tap.
(b) Determine the angular speed of the student–stool–masses system immediately after the tap. Assume the other mass was not struck and is momentarily at rest with respect to the student.
(c) The tapped mass slides frictionlessly in a radial groove so it cannot move tangentially relative to the stool after the tap. Describe qualitatively what happens to the angular momentum of the mass and to the angular speed of the student as the mass comes to rest relative to the stool.
(d) After the system reaches a common angular speed, the student extends both arms back outward to the original radius of 0.75m. Compute the final angular speed of the system, and discuss whether the friend’s tap ultimately changes the student’s rotational kinetic energy compared with a scenario in which no tap occurred.