To understand the definition and the meaning of moment of inertia; to be able to calculate the moments of inertia for a group of particles and for a continuous mass distribution with a high degree of symmetry. By now, you may be familiar with a set of equations describing rotational kinematics. One thing that you may have noticed was the similarity between translational and rotational formulas. Such similarity also exists in dynamics and in the work-energy domain. For a particle of mass m moving at a constant speed v, the kinetic energy is given by the formula K=12mv2. If we consider instead a rigid object of mass m rotating at a constant angular speed ω, the kinetic energy of such an object cannot be found by using the formula K=12mv2 directly: different parts of the object have different linear speeds. However, they all have the same angular speed. It would be desirable to obtain a formula for kinetic energy of rotational motion that is similar to the one for translational motion; such a formula would include the term ω2 instead of v2. Such a formula can, indeed, be written: for rotational motion of a system of small particles or for a rigid object with continuous mass distribution, the kinetic energy can be written as

K=12Iω2.

Here, I is called the moment of inertia of the object (or of the system of particles). It is the quantity representing the inertia with respect to rotational motion. It can be shown that for a discrete system, say of nparticles, the moment of inertia (also known as rotational inertia) is given by

I=∑ni=1mir2i.

In this formula, mi is the mass of the ith particle and ri is the distance of that particle from the axis of rotation. For a rigid object, consisting of infinitely many particles, the analogue of such summation is integration over the entire object:

I=∫r2dm.

Required:
On which of the following does the moment of inertia of an object depend?

a. linear speed
b. linear acceleration
c. angular speed
d. angular acceleration
e. total mass
f. shape and density of the object
g. location of the axis of rotation