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What are the units of moment of inertia? Of angular speed ? Of angular momentum? Of linear momentum?

Short Answer

Expert verified

The unit of moment of Inertia iskg.m2

The unit of angular speed is rad/s

The unit of angular momentum iskg.m2/s

The unit of Linear momentum is kg.m/s

Step by step solution

01

Definition of Moment of Inertia, Angular speed, Angular Momentum and Linear Momentum.

The moment of inertia is a quantitative measure of a body's rotational inertia鈥攖hat is, the body's resistance to having its speed of rotation along an axis changed by the application of a torque (turning force).

The rate of change of angular displacement is known as angular speed.

The rotating inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system is described by angular momentum.

Linear Momentum is the momentum of translation, which is a vector quantity equal to the product of mass and velocity of the center of mass in classical physics.

02

Unit of Moment of Inertia and the unit of Angular speed

The moment of inertia of the disk of mass M and radius r is

I=Mr2

Here unit of mass is kg unit of radius is meter (m) Therefore the unit of moment of inertia iskg.m2

The unit of angular speed is rad/s

03

Unit of Angular momentum and the unit of Linear Momentum

The angular momentum of the system with moment of inertia and velocity can be expressed as

L=I

Here unit of moment of inertia is kg.m2and unit of angular speed is rad/s

By combining these units, we get unit of angular momentum askg.m2/s

The linear momentum of the body of mass moving with speed v can be expressed as

p=mv

Here the unit of mass is kg and unit of speed is m/s

By combining these units, we get of linear momentum as kg.m/s

Hence, the unit of Moment of Inertia, Angular speed, Angular Momentum and Linear Momentum is kg.m2,rad/s,kg.m2/sandkg.m/srespectively.

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Most popular questions from this chapter

An amusing trick is to press a finger down on a marble on a horizontal table top, in such a way that the marble is projected along the table with an initial linear speed vand an initial backward rotational speed about a horizontal axis perpendicular to v. The coefficient of sliding friction between marble and top is constant. The marble has radius R. (a) if the marble slides to a complete stop, What was in terms of vandR? (b) if the marble, skids to a stop, and then starts returning toward its initial position, with a final constant speed of (3/7)v,What was in terms of vandR? Hint for part (b): when the marble rolls without slipping, the relationship between speed and angular speed isv=R.

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(a) Which of the following statements are true, for angular momentum relative to the axle of the wheel? (1) Just before the collision, r=0.42/2=0.4cos(45)(for the clay). (2) The angular momentum of the wheel is the same before and after the collision. (3) Just before the collision, the angular momentum of the wheel is0. (4) The angular momentum of the wheel is the sum of the angular momentum of the wheel + clay after the collision is equal to the initial angular momentum of the clay. (6) The angular momentum of the falling clay is zero because the clay is moving in a straight line. (b) Just after the collision, what is the speed of one of the balls?

Determine both the direction and magnitude of the angular momentum of the particle in Figure 11.13, relative to the locations D, E,F, G, and H. We've already analyzed the angular momentum relative toA, B, and C in the example given above. Notice how the magnitude and direction of the angular momentum relative to the different locations differ in magnitude and direction.

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