A Comprehensive Guide to Understanding Circular Motion
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1) A rigid body is spinning with an angular velocity of 4 rad/sec, about an axis parallel to (3j-k) passing through the point (O) (i+3j-k). Find the velocity of the particle at the point ‘P’ (4i-2j+k) ?
2) Find the angular speed A relative to B, in both the cases
3) A bob attached to a light string is oscillating in a vertical plane. It’s acceleration at extreme and mean position will be equal, for what value of the angular amplitude (θ)?
4) A point moves with deceleration along the circle of radius R so that at any time, its at, ac are equal in magnitude. If at t = 0, velocity of the point = V0, then express its velocity as a function of time (t) and distance covered (S)?
5) A particle moves uniformly with speed ‘u’ along a parabolic path y = bx2, where ‘b’ is a positive constant. Find the acceleration of the particle and radius of curvature of the path at x =0 ?
6) The velocity and acceleration of a particle moving on a circular path are given by, V = (3i + 2j) m/sec, a = (-4i + 2j) m/sec2. What nature of motion it is ?
7) A particle starts moving on a circle of radius ‘R’ and has a centripe- -tal acceleration ‘a’. It’s centripetal and tangential acceleration will be equal after what time ?
8) A body starts moving on the circumference of the circle of radius √2 mt, with constant angular acceleration of π/4 rad/sec2. Find the average velocity as it completes quarter circle?
9) A bob is attached to one end of a string, other end of which is fixed at Peg ‘A’. The bob is taken to the position shown in figure, from there it is projected with minimum speeds Vc, Va in clockwise and anti clockwise directions so as hit a Peg B. What is the ratio betw- -een Vc and Va ?
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