Moment of Inertia: Understanding Rotational Motion Property

Which of the entries in Table 10.2 applies to finding the moment of inertia of a coin turning about an axis through its center and perpendicular to its faces?

What is the moment of inertia?

Answer:

The correct entry in Table 10.2 for finding the moment of inertia of a coin turning about an axis through its center and perpendicular to its faces is option d) Coin: \(I_{CM} = \frac{1}{2} MR^{2}\).

Moment of Inertia:

A rigid body's moment of inertia, also referred to as its mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia, is a property that establishes the torque required to achieve a desired angular acceleration about a rotational axis, much like mass establishes the force required to achieve a desired acceleration. Depending on the axis selected and the distribution of the body's mass, a change in the body's rate of rotation will need a greater torque for larger moments.

Among the options provided, the moment of inertia formula for a coin turning about an axis through its center and perpendicular to its faces is given by \(I_{CM} = \frac{1}{2} MR^{2}\). This formula takes into account the specific shape and distribution of mass in a coin's structure to calculate the rotational inertia.