Question

In this problem, you will answer several questions that will help you better understand the moment of inertia, its properties, and its applicability. It is recommended that you read the corresponding sections in your textbook before attempting these questionsn 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. b) What is the moment of inertia of particle a? mr2 9mr2 10mr2 undefined: an axis of rotation has not been specified.

Answer 1

The moment of inertia of an object depends on the following;

1. angular speed
2. angular acceleration
3. total mass
4. shape and density of the object
5. location of the axis of rotation.

The moment of inertia of particle A is Undefined because an axis of rotation has not been specified.

What is the moment of inertia?

The moment of inertia also called the mass moment of inertia or rotational inertia, is a physical quantity that measures an object's resistance to changes in its rotational motion. It is the rotational equivalent of mass in linear motion.

The answer for the second one is "undefined because an axis of rotation has not been specified." We need to know the location of the axis of rotation relative to the particle to calculate its moment of inertia.

Answer 2

a) Total mass form, density and axis of rotation location are True

b) I = m r²

Step-by-step explanation:

a) The moment of inertia is the inertia of the rotational movement is defined as

I = ∫ r² dm

Where r is the distance from the pivot point and m the difference in body mass

In general, mass is expressed through density

ρ = m / V

dm = ρ dV

From these two equations we can see that the moment of inertia depends on mass, density and distance

Let's examine the statements, the moment of inertia depends on

- Linear speed False

- Acceleration angular False

- Total mass form True

- density True

- axis of rotation location True

b) we calculate the moment of inertia of a particle

For a particle the mass is at a point whereby the integral is immediate, where the moment of inertia is

I = m r²