Imagine a ball rolling down a hill without friction. To measure the moment of inertia, which of...

Question:

Conservation of mechanical energy; Rolling motion

Conservation of mechanical energy

• In an isolated system, the total mechanical energy of an object remains constant in time.
• The energy can transform from potential into kinetic or vice-versa, but their sum remains constant:

{eq}\Delta U = - \Delta K{/eq}, where U is potential energy and K is kinetic energy.

Rolling motion

• An object is rolling when it has both translational motion (it moves on a straight line) and rotational motion (it rotates about an axis) at the same time.
• The rolling motion requires a small amount of friction, enough to prevent slipping but not more than that (in other words, it does not dissipate energy as heat).
• In rolling motion, the total kinetic energy, K, is given by: {eq}K_{tot} = K_{translation} + K_{rotation} {/eq}

• If the rolling is without slipping, the angular speed and the speed of the mass center of the rolling object are related through the formula: {eq}\omega = \dfrac{v_{cm}}{R} {/eq}

Answer and Explanation:

Diagram:

The following diagram illustrates the system and the energies in the key points.

Elements in the diagram:

• i and f stand for initial and...

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