Chapter 12, Problem 10A

Distinguish between linear momentum and angular momentum.

To determine

To explain: The differences between linear momentum and the angular momentum.

Explanation of Solution

Introduction:

Momentum of the object is basically mass of an object in motion. Every moving object will have momentum. Momentum is a vector quantity that is it has both magnitude and direction. There are two types of momentum namely angular and linear momentum.

Angular Momentum:

When an object is moving in a circular path, the object is said to be in rotational motion and the momentum possessed by an object in rotational motion is called as angular momentum.

Consider an object is moving with the angular velocity $\omega$ in a circular path at a radial distance $r$ from the axis of the rotation.

The relation for the angular momentum $\left(L\right)$ of the object is,

  $L=I\omega$

Here, $I$ is the system’s moment of inertia and $\omega$ is the angular velocity.

The object’s angular momentum is a vector quantity acts in a direction at $90°$ to the plane of rotation.

The SI unit of angular momentum is $\text{kg}\cdot {\text{m}}^2\text{/s}$ .

Example: The planets movement around the sun in circular path.

Linear Momentum:

When an object is moving in a linear or straight path, the object is said to be in linear motion and the momentum possessed by an object in linear motion is called as linear momentum.

Consider an object of mass $m$ is moving with a velocity $v$ in a straight path.

The relation for the linear momentum $\left(p\right)$ of the object is,

  $p=mv$

The object’s linear momentum of an object is a vector quantity acts in a direction of the velocity vector.

The SI unit of linear momentum is $\text{kg}\cdot \text{m/s}$ .

Example: A car moving in a straight road.