Question

The direction of net acceleration if a particle has tangential acceleration is:
A. Towards the center
B. Makes some angle θ with the radius vector.
C. Along the tangent
D. Along the axis of location

Answer 1

Hint: Try and remember the other acceleration that will be acting on the particle. It will be the acceleration acting towards the center of the circle. They will act at 90 degrees to each other. Use this to conclude the solution.

Complete step by step answer:
As we know, that tangential acceleration is due to change in tangential speed.
Thus the particle in non-uniform circular motion will have 2 acceleration acting on it. One will be along the radius of the circle and the other will be along the tangent, such that both of the accelerations will be perpendicular to each other. The net acceleration of their 2 perpendicular accelerations will be thus the vector sum of both the accelerations.
Thus the net acceleration will be clearly at an angle θ with the radius vector.

So, the correct answer is “Option B”.

Note: Try to visualize the problem for better understanding of the solution. The 2 acceleration acting perpendicular will have the net acceleration at angle ‘θ’. Additionally, the tangential acceleration tries to pull the particle outwards and the acceleration towards the center pulls it inwards. In non-uniform circular motion, the magnitude of the angular velocity changes over time.