3- D Kinematics

Now, since the direction of is fixed i.e., along the axis and only magnitude can change has the same direction as . Hence, has the same direction as . Thus in equation (i), the first component is the tangential component of the acceleration.

If we indicate by , the angular acceleration, then tangential component component may be written as . i.e., the tangential component of the particle is angular acceleration of a particle is the angular acceleration times the perpendicular distance from the axis.

Let us look at the other component, . This component is in the plane of rotation ( normal to fixed axis) and perpendicular to tangetial direction.

It can be easily shown that magnitude of is .

Since V and a are perpendicular to and ,