Rotational Kinetic Energy:- K r = ½ Iω 2 = ½ mr 2 ω 2.It is same whether the body is at rest, rotating slowly or rotating fast about the given axis. (iv) It does not depend upon the state of motion of rotating body. (iii) Moment of inertia of a body should always be referred to as about a given axis, since it depends upon distribution of mass about that axis. (ii) Distribution of mass about the axis of rotation ![]() Moment of Inertia (Rotational Inertia) I:- Moment of Inertiaof a body, about a given axis, is defined as the sum of the products of the masses of different particles constituting the body and the square of their distances from the axis of rotation. Rigid Body:-A rigid body consists of a number of particles confined to a fixed geometrical shape and size in such a way that the distance between any pair of particles always remains constant. So, a = √ a t 2 + a c 2 Rotational Motion (iii) The total acceleration is the vector sum of the tangential and centripetal acceleration. (ii) Normal acceleration or centripetal acceleration a c changes the direction of the velocity vector and is defined as, a c = v 2 / r (i) Tangential acceleration a t changes the magnitude of velocity vector and is defined as, a t = dv / dt (d) The acceleration vector has two components. (c) The acceleration vector is not perpendicular to the velocity vector. (b) The velocity vector is always tangential to the path. (a) The velocity changes both in magnitude as well as in direction. (c) Condition for leaving circular path:- √2 gl < V A ?√5 gl (b) Condition for oscillation:- V A ?√2 gl (a) For lowest point A and highest point B, T A – T B = 6 mg The minimum tension in the string, at the lowest point, required to take the body around the vertical circle is equal to six times the weight of the body. The minimum velocity of the body, at the lowest point, required to take the body round a vertical circle is √5 gr. ![]() Motion in a vertical circle/looping the loop:. Time period of conical pendulum:- T = 2π √ lcos θ/ g (b) Radius of curvature:- Smaller the radius, greater is the angle with the vertical. (a) Velocity of the cyclist:- Greater the velocity, greater is his angle of inclination with the vertical. Bending of Cyclist:- θ = tan -1 ( v 2/ rg).Road offering frictional resistance, v max = √ rg( µ+tanθ/1- µtanθ) Road offering no frictional resistance, θ = tan -1 ( v 2/ rg) They cannot be termed as action and reaction since action and reaction never act on same body. Magnitude of centrifugal force is,Ĭentripetal and centrifugal forces are equal in magnitude and opposite in direction. Centrifugal force:-Centrifugal force is the fictitious force which acts on a body, rotating with uniform velocity in a circle, along the radius away from the center.It acts always along the radius towards the center. If f is the frequency, the particle describes 2πf radians per second.Ĭentripetal force:-The force, acting along the radius towards the center, which is essential to keep the body moving in a circle with uniform speed is called centripetal force. Frequency:- The number of rotations made by the particle per second is called the frequency of rotation.Time period:- It is the time taken by the particle to complete one rotation.(c) Angular velocity after a certain rotation:- ω 2 – ω 0 2 = 2 αθ (b) Angular displacement after t second:- θ = ω 0 t + ½ αt 2 ![]() (a) Angular velocity after a time t second:- ω= ω 0+ αt Relation betweenlinear acceleration ( a), angular velocity ( ω) and linear velocity (v):.Relation between linear acceleration (a) and angular acceleration (α):. Relation between linear velocity ( v) and angular velocity ( ω):. Uniform Circular Motion:-Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant.Revision Notes on Circular& Rotational Motion Circular Motion:.
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