Question

Which of the following is NOT true? a. The higher the moment of inertia, the greater the resistance to changes in angular velocity. b. The higher the moment of inertia, the slower something will roll down an incline. c. The lower the moment of inertia, the easier it is to change the angular velocity. d. The lower the moment of inertia, the slower something will roll down an incline.

Answer 1

Answer:

Explanation:

The moment of inertia is the integral of the product of the squared distance by the mass differential. Is the mass equivalent in the rotational motion

a) True. When the moment of inertia is increased, more force is needed to reach acceleration, so it is more difficult to change the angular velocity that depends proportionally on the acceleration

b) True. The moment of inertia is part of the kinetic energy, which is composed of a linear and an angular part. Therefore, when applying the energy conservation theorem, the potential energy is transformed into kinetic energy, the rotational part increases with the moment of inertia, so there is less energy left for the linear part and consequently it falls slower

c) True. The moment of inertial proportional to the angular acceleration, when the acceleration decreases as well. Therefore, a smaller force can achieve the value of acceleration and the change in angular velocity. Consequently, less force is needed is easier