In this exercise, consider a particle moving on a circular path of radius b described by r(t) = b cos(ωt)i + b sin(ωt)j, where ω = du/dt is the constant angular velocity. find the acceleration vector and show that its direction is always toward the center of the circle.

Acceleration of the particle =

Step-by-step explanation:

We are given the position vector of a particle moving in a circle of radius b units.

r(t) = b cos(ωt)i + b sin(ωt)j

Velocity , v == -bω sin(ωt)i + bω cos(ωt)j

The magnitude of velocity, v =

Squaring both sides,

Since = 1

The acceleration towards the centre is called the centripetal acceleration and is given by

a =

a =

a =