System of Particles and Rotational Motion Test

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System of Particles and Rotational Motion Test - 6

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Question 1
1 / -0

The parallel axis theorem gives the moment of inertia ______________ to the surface under consideration.

A
planar

B
non-planar

C
parallel

D
perpendicular

Solution

Parallel axis for any plane is used to add the two mutually perpendicular moment of inertias for planes. It gives a moment of inertia perpendicular to the surface of the body. That is the moment of inertia perpendicular to the surface in consideration.
Question 2
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Which of the following statement is not true about the moment of inertia?

A
is analogues with mass

B
does not depend where the mass is located

C
resistance to change in rotational inertia

D
is directly proportional to the square of the distance.

Solution

Moment of inertia is given the symbol I. For a single body of mass m, rotating at radius r from the axis of rotation the moment of inertia is defined as;

I = mr²

Where I is the moment of inertia, r is the radius and m is the mass the body

and consequently rotational inertia has SI units Kg.m²

Moment of inertia is also commonly known as rotational inertia as it is considered as the mass analogous to the rotational motion.

The moment of inertia is directly proportional to the square of the distance of the mass from the axis of rotation.

Thus moment of inertia does depend on the location of the mass from the axis of rotation.
Question 3
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The ___________ of a body about an axis may be defined as the distance from the axis of a mass point whose mass is equal to the mass of the whole body.

A
moment of inertia

B
radius of rotation

C
radius of gyration.

D
center of gravity

Solution

As a measure of the way in which the mass of a rotating rigid body is distributed with respect to the axis of rotation, we can define a new parameter, the radius of gyration. It is related to the moment of inertia

and the total mass of the body.

I = mk²

Where m is equal to the mass of the whole body

And k depends on the geometric property of the body and the axis of rotation. It is defined as the radius of gyration.
Question 4
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The practical use of the moment of inertia can be seen in the machines and big steam engines that produce rotational motion have a large disc with large moment of inertia, called __________.

A
gears

B
shaft

C
flywheel

D
governors

Solution

The property of this extremely important quantity I as a measure of rotational inertia of the body has been put to a great practical use. The machines, such as steam engine and the automobile engine, etc., that produce rotational motion have a disc with a large moment of inertia, called a flywheel.

Because of its large moment of inertia, the flywheel resists the sudden increase or decrease of the speed of the vehicle. It allows a gradual change in the speed and prevents jerky motions, thereby ensuring a smooth ride for the passengers on the vehicle.