When a particle moves in a plane such that its distance from a fixed (or moving) point remains constant, then its motion is known as circular motion with respect to that fixed (or moving) point. The fixed point is called centre, and the distance of particle from it is called radius.
~ Circular Motion
KINEMATICS OF CIRCULAR MOTION
Angular Position
To decide the angular position of a point in space we need to specify (i) origin and (ii) reference line. The angle made by the position vector w.r.t. origin, with the reference line is called angular position.
- Clearly angular position depends on the choice of the origin as well as the reference line.
- Circular motion is a two dimensional motion or motion in a plane
Angular Displacement
Angle through which the position vector of the moving particle rotates in a given time interval is called its angular displacement. Angular displacement depends on origin, but it does not depends on the reference line. As the particle moves on above circle its angular position changes.
Remember
- Angular displacement is a dimensionless quantity. Its SI unit is radian, some other units are degree and revolution. 2pi rad = 360° = 1 rev
- Infinitesimally small angular displacement is a vector quantity, but finite angular displacement is a scalar, because while the addition of the Infinitesimally small angular displacements is commutative, addition of finite angular displacement is not.
- Direction of small angular displacement is decided by right hand thumb rule. When the fingers are directed along the motion of the point then thumb will represents the direction of angular displacement
Angular velocity
Average Angular Velocity
Since angular displacement is a scalar, average angular velocity is also a scalar.
Instanteneous angular velocity
It is the limit of average angular velocity as ◆t approaches zero.
Since infinitesimally small angular displacement is a vector quantity, instantaneous angular velocity is also a vector, whose direction is given by right hand thumb rule.
- Angular velocity has dimension of [T-¹] and SI unit rad/s.
- For a rigid body, as all points will rotate through same angle in same time, angular velocity is a characteristic of the body as a whole, e.g., angular velocity of all points of earth about earth’s axis is (2pi/24) rad/hr.
- If a body makes ‘n’ rotations in ‘t’ seconds then average angular velocity in radian per second. If T is the period and ‘f’ the frequency of uniform circular motion.
