At an instant, a particle moving on a circle has tangential acceleration aₜ = 3 m/s² and radial acceleration $a_c$ = 4 m/s². The angle φ made by the net acceleration with the inward radial direction is:
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Question

At an instant, a particle moving on a circle has tangential acceleration aₜ = 3 m/s² and radial acceleration $a_c$ = 4 m/s². The angle φ made by the net acceleration with the inward radial direction is:

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G1 Physics · Accepted Answer

The net acceleration is the vector sum of mutually perpendicular components a_c (radially inward) and aₜ (tangential). If φ is measured from the inward radial direction, tanφ = aₜ/a_c = 3/4. Hence φ = tan⁻¹(3/4).

At an instant, a particle moving on a circle has tangential acceleration aₜ = 3 m/s² and radial acceleration a_c = 4 m/s². The angle φ made by the net acceleration with the inward radial direction is: