CBSE Class 11-science Physics System of Particles and Rotational Motion
Centre of Mass
1. Rigid body: Distances between different particles of the body do not change.
2. Pure rotation: Every particle of the rigid body moves in a circle with same angular velocity at any instant of time.
3. Pure translation: Every particle of the body moves with the same velocity at any instant of time.
Conservation of Angular Momentum
1. Angular momentum L depends on mass, velocity perpendicular to a point on the axis, and radius vector r:2. Angular momentum of a system is also given as: L=I w
3. If the net resultant external torque acting on an isolated system is zero, then total angular momentum L of system should be conserved.
Dynamics of Rotational Motion
1. Torque about a point on a fixed axis t = I aandnbsp;andnbsp;
2. The total work done by the net force during aandnbsp; finite rotation: W = t q
3. Instantaneous pow
Kinematics of Rotational Motion1. The equation analogous to v = v0+ at in linear motion isandnbsp; andomega; = andomega;0 + at
Moment of Inertia
andnbsp;1. The moment of inertia of a rigid body about an axis is defined by the formulaandnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp;andnbsp; where ri is the perpendicular distance of the ith point of the body from the axis.
2. The kinetic energy of rotation is K= (andfrac12; )Iandomega;2.
Equilibrium of Rigid BodyFor a body at equilibrium: Resultant of all the external forces and torques must respectively be zero.
Centre of gravity is the location where the whole weight of the body to be assumed is concentrated.
At equilibrium, the centre of gravity should always lie at or directly above or below the point of suspension.
Angular MomentumThe angular momentum of a system of andlsquo;nandrsquo; particles about the origin:
Torque1. Torque is the rotational analogue of force in translational motion.
Kinematic Variables in RotationDefine Angular displacement, Angular velocity and Angular acceleration. Establish the mathematical relation between angular and linear variables.
Motion of Centre of Mass
andnbsp;1. Velocity of the centre of mass of a system of particles:andnbsp;andnbspandnbsp;andnbsp;andnbsp;andnbsp; , where is the linear momentum of the system.
Rolling MotionIntroduce rolling motion as a combination of rotational and translational motions. Quantify Kinetic energy of a body in rolling motion.