Question

A carnival merry-go-round has a large disk-shaped platform of mass 120 kg that can rotate about a center axle. A 60- kg student stands at rest at the edge of the platform 4.0 m from its center. The platform is also at rest. The student starts running clockwise around the edge of the platform and attains a speed of 2.4 m/s relative to the ground.

A) Determine the rotational velocity of the platform.

B) Determine the change of kinetic energy of the system consisting of the platform and the student.

Answer 1

Given data The mass is, M 120 kg m-60kg The radius is, r4.0 m The speed is, v= 2.4 ms The moment of inertia of the platform is, 2 = (0.5)(120)(4.0) = 960 kg.m The moment of inertia of the platform is along with student along the edge of the disk is, = (0.5)(120)(4.0). (60)(4.0) = 1920 kgm. The angular momentum of the student is, L-mvr -(60) (2.4)(4.0) = 576 kg.m/s Using conservation of angular momentum, af- 576 1920 - 0.3 rad/s The rotational velocity of the platform obtained as follows, 960 1920 0.5 m/s The change in kinetic energy of the system is, (0.5)960)(05)-(0.5)1920) 03) -33.6 J