o understand the definition and the meaning of moment of inertia; to be able to

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o understand the definition and the meaning of moment of inertia; to be able to calculate the moments of inertia for a group of particles; to relate moment of inertia to kinetic energy.

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 androtational 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 , the kinetic energy of such an object cannot be found by using the formula K=12mv2 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 2 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=12I2.

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 of n particles, 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 riis the distance of that particle from the axis of rotation.

Part A

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

Check all that apply.

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Consider the system of two particles, a and b, shown in the figure. Particle a has mass m, and particle b has mass 2m.

(Figure 1)

Part B

What is the moment of inertia Ia of particle a?

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o understand the definition and the meaning of moment of inertia; to be able to calculate the moments of inertia for a group of particles; to relate moment of inertia to kinetic energy.

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 androtational 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 , the kinetic energy of such an object cannot be found by using the formula K=12mv2 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 2 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=12I2.

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 of n particles, 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 riis the distance of that particle from the axis of rotation.

Part A

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

Check all that apply.

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

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Incorrect; Try Again; 19 attempts remaining

Consider the system of two particles, a and b, shown in the figure. Particle a has mass m, and particle b has mass 2m.

(Figure 1)

Part B

What is the moment of inertia Ia of particle a?

What is the moment of inertia  of particle a?
mr2 9mr2 10mr2 undefined: an axis of rotation has not been specified.

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Explanation / Answer

Part A

Basic eqution of moment of inertia is MR^2

So it depends on follwing

Total mass

shape and density of the object

location of the axis of rotation

According to formula it directly proportional to mass and it does depend on mass distribution because we need to know small of amount of mass and where it is located so shape and density also required and r is the distance from axis of rotation so we required this also.

Part B

undefined: an axis of rotation has not been specified

as explained in part A we need axis of rotation for moment of inertia

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