Question

A particle moves in a circle of radius 4.0 cm clockwise at constant seed of 2 cms^-1. If \(\hat x\) and \(\hat y\) are unit acceleration vectors along X-axis and Y-axis, respectively, find the acceleration of the particle at the instant half-way between P and Q in the Figure.

Answer 1

At point the acceleration will be centripetal acceleration which is radially directed towards point O. i.e.

Physically: \(\vec a = \frac {v^2}r (-\hat e_r)\)

Remember \(\hat e_r\) and \(\hat e_t\) are the unit vectors along radial and tangential directions respectively.

So in this case also \(\vec {a_A} = \frac {v^2}r (-\hat e_r)\)

Now, since he point is in between the points P and Q,