What is the effect of changing the platform from disk to hoop on the angular velocity of the platform? Explain the rationale using the law of conservation of angular momentum.
A. It decreases the angular velocity to one-half of its original value. The rationale: There is no force applied on the disk hence no net torque. When the net torque is zero, the angular momentum is conserved. Therefore, when the moment of inertia is doubled (by switching from disk to hoop), the angular velocity will decrease to one-half of its value in order to maintain the same initial angular momentum.
B. The angular velocity stays the same. The rationale: There is no force applied on the disk hence no net torque. When the net torque is zero, the angular velocity is conserved. Therefore, when the moment of inertia is doubled (by switching from disk to hoop), the angular velocity will stay the same in order to maintain its conservation law.
C. It decreases the angular velocity to one-fourth of its original value. The rationale: There is no force applied on the disk hence no net torque. When the net torque is zero, the angular velocity is conserved. Therefore, when the moment of inertia is doubled (by switching from disk to hoop), the angular velocity will stay the same in order to maintain its conservation law.
D. It increases the angular velocity to double its original value. The rationale: There is no force applied on the disk hence no net torque. When the net torque is zero, the angular momentum is conserved. Therefore, when the moment of inertia is doubled (by switching from disk to hoop), the angular velocity will double its value in order to maintain the same initial angular momentum.