Question

A ball, which is initially at rest, starts rotating around a fixed point. The ball has a constant angular acceleration. You need to know that the radial acceleration of the ball aradarad is proportional to ball's angular displacement θ

Find the angular displacement of the ball if its resultant acceleration makes an angle of 40 ∘ with the radial direction?

Answer 1

given : resultant acceleration makes an angle of 40 degree with the radial direction.

angular acceleration is constant.

initial angular velocity is zero.

------(i) [where = tangenial acceleration, = radial acceleration]

Relation between tangential acceleration and angular acceleration :

-----(ii) [R = radius]

Relation between radial acceleration and angular velocity :

-------(iii)

using kinematics of circular motion :

[ = final angular velocity = , = initial angular velocity = 0, = angular acceleration, = angular displacement]

[using (ii) and (iii)

[using (i) ]

[answer]