For a particle of mass moving at a constant speed , the kinetic energy is given

Question

For a particle of mass moving at a constant speed , the kinetic energy is given by the formula . If we consider instead a rigid object of mass rotating at a constant angular speed , the kinetic energy of such an object cannot be found by using the formula directly, since 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 instead of .
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
Here, 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 of particles, the moment of inertia (also known as rotational inertia) is given by
In this formula, is the mass of the ith particle and is the distance of that particle from the axis of rotation.
On which of the following does the moment of inertia of an object depend?
Check all that apply.
linear speed
linear acceleration
angular speed
angular acceleration
total mass
shape and density of the object
location of the axis of rotation

Explanation / Answer

total mass shape and density of the object location of the axis of rotation unlike mass, the moment of inertia depends not only on the amount of matter in object but also on the distribution of mass in space. The moment of inertia is also depends on the axis of rotation. The object, rotating with the same angular speed may have different kinetic energy depending on the axis of rotation.

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