Name: Inertial Frames of Reference
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: Imagine if you are on a bus or a train, can you say you are in an inertial frame of reference? If yes, how can you predict it? Let us explore more in this vi...

Question

Define angular displacement, angular velocity. Find the relation between angular velocity and linear velocity.

Accepted Answer

Angular displacement of a body is the angle in radians (degrees, revolutions) through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis. It is the angle of the movement of a body in a circular path. It is a vector quantity, which means that it has both magnitude and direction. The unit for this is Radian or Degrees.

$θ = \frac{∆ s}{r}$

Angular velocity is the rate of velocity at which an object or a particle is rotating around a centre or a specific point in a given time period. It is also known as rotational velocity. Angular velocity is measured in angle per unit time or radians per second (rad/s). It is also a vector quantity.

Mathematically, $ω = \frac{∆ θ}{∆ t}$

Angular velocity $ω$ is analogous to linear velocity $v$ . To find the precise relationship between angular and linear velocity, consider the diagram above. For arc length $∆ s$ in a time $∆ t$ , and so it has a linear velocity $v = \frac{∆ s}{∆ t}$

From $∆ θ = \frac{∆ s}{r}$

Substituting this into the expression for $v$ gives

$v = \frac{r ∆ θ}{∆ t} = r ω$

We can write this relationship in two different ways: $v = r ω or ω = \frac{v}{r}$

Define angular displacement, angular velocity. Find the relation between angular velocity and linear velocity.

Important Questions on Motion of a Particle

Learn and Prepare for any exam you want !