Hoekige en lineaire grootheden met elkaar in verband brengen - I

All the linear motion variables have a counterpart in rotational motion. Consider a ball tied to a string of length r, rotating such that the axis of rotation lies in the plane perpendicular to its plane of motion.

When the ball changes its angular displacement by θ, the linear distance it travels is equal to the arc length s.

At any point during the motion, the linear distance is directly proportional to the angular distance θ. For 2π changes in angular distance, the corresponding arc length is 2π times the radius.

Now, take the time derivative of the equation. As the radius of the circle is constant, the rate of change of arc length is proportional to the rate of change of angular displacement. Thus, a relationship between instantaneous linear velocity and instantaneous angular velocity is obtained.

The direction of the velocity of the ball is tangential to the circular motion, hence termed as tangential velocity.