At an instant, a particle has speed 12 m/s and acceleration magnitude 6 m/s². The angle between velocity and acceleration is 60°. If the radius of curvature is 8√N m, find N.

Question

G1 Physics · Accepted Answer

The normal component of acceleration is aₙ = a sin60° = 6×(√3/2) = 3√3 m/s². Radius of curvature R = v²/aₙ = 144/(3√3) = 48/√3 = 16√3 m. Comparing with R = 8√N gives 8√N = 16√3 ⇒ √N = 2√3 ⇒ N = 12.