Physics > Circular Motion > 1.0 Introduction
Circular Motion
1.0 Introduction
1.1 Angular Variables
1.2 Kinematic equation for circular motion
1.3 Relation between angular and linear variables
1.4 Unit vectors along the radius and tangent
1.5 Velocity and acceleration of particle in circular motion
2.0 Dynamics of circular motion
3.0 Motion in a vertical circle
4.0 Rigid body rotating in a vertical circle
5.0 Circular turning of roads
6.0 Conical Pendulum
7.0 Death well
8.0 Rotor
9.0 Bending of a cyclist or motorcyclist while taking turn
10.0 Centrifugal force
1.4 Unit vectors along the radius and tangent
1.2 Kinematic equation for circular motion
1.3 Relation between angular and linear variables
1.4 Unit vectors along the radius and tangent
1.5 Velocity and acceleration of particle in circular motion
Consider a particle moving in a circular path of radius $r$ with center at $O$ .
The angular position of particle at point $P$ at any time $t$ is $\theta $.
Let us define two unit vectors,
- ${\widehat e_r}$ is radial unit vector along the radius i.e. along $OP$
- ${\widehat e_t}$ is tangential unit vector at point $P$
Since it is a unit vector, its magnitude is always unity i.e. 1
$$\left| {{{\widehat e}_r}} \right| = \left| {{{\widehat e}_t}} \right| = 1$$
Resolving the above two unit vectors into its component we get,
$$\begin{equation} \begin{aligned} {\widehat e_r} = \cos \theta \widehat i + \sin \theta \widehat j \\ {\widehat e_t} = - \sin \theta \widehat i + \cos \theta \widehat j \\\end{aligned} \end{equation} $$
