Name: Equations of Motion in Rotational Motion
Uploaded: 2019-07-19
Duration: 4 min 17 s
Description: In this video, we will learn about the basic equations of rotational motion with constant angular acceleration with easy examples.

Question

Define angular displacement and angular velocity. Find the relation between angular velocity and linear velocity. Also, show that in circular motion the linear velocity is along the tangential direction.

Accepted Answer

Angular displacement: The angle in radians (or degree or in revolutions) through which a point or a line is rotated in a specified sense in a specified direction is known as angular displacement. It is denoted as $θ$ .

Angular velocity: The vector quantity describing the rate of change of angular displacement with time, giving a clear idea about the rotational speed of the object and the axis about which the object is rotating is known as angular velocity. Its is denoted as $ω$ .

Let us assume the following for a body moving in a circular path:

$S be the linear displacement of the body, r be the radius of the circular path, θ be the angular displacement, v is the linear velocity, and ω is the angular velocity of the body.$

We know that $S = r θ$ .

Differentiating both sides with respect to time, we get:

$\frac{d S}{d t} = r \frac{d θ}{d t} \Rightarrow v = r ω Or, Linear velocity = radius \times angular velocity$

This is the required relation between linear and angular velocity of a body.

Velocity is the instantaneous rate of change of displacement. So at any instant in circular motion the displacement of the body takes place along the tangent of the circle. Hence, this indicates the velocity to be tangential.

Define angular displacement and angular velocity. Find the relation between angular velocity and linear velocity. Also, show that in circular motion the linear velocity is along the tangential direction.

Important Questions on Circular Motion

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