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MIND PALACE UDIT GUPTA
WELCOME TO THE 4RD MIND PALACE! TODAY WE DISCUSS ROTATIONAL DYNAMICS DONT FORGET TO CHECK THE SPECIAL GLASSES &PLUS COURSED Apos Other bookom unacademy Home minus oday Serch Coss Topis&Educa Browse Courses ALL Railway Examinations Class 12 NTA-UGCNET GATE (Civil RPSC CTET MPSc SSC CGL IT JEE Exams CAT UPSC CSE GATE (CS and IT) CDS NDA/ AFCAT IIT JEE Crash Course on Physics through 750 Important Questions Last date to apply is 29th Oct Soil, Classification and Distribution Exam Oriented Discussion on Numbers and Operation Understanding Fluid Flow through Top Festivais and Fairs of Rajasthan 7,500 21 21 t Udit Gupta
Rigid Body Motion During such motion, all the particles have the same displacement (s), velocity (v) and acceleration (a) during any interval and at any instant. Pure translational motion For a system of particles: mi+m2+ mu-m12+ m11+m272+ Position, em- Pure rotational motion Velocity, Ucrn min+m2v2+.. Acceleration, ammi@it m2azt m1+m2+. Pure rolling motion Translation Rotation If Fext 0, then, vcm constant. Every point of the body moves in a circle whose centre lies on the axis of rotation.
Pure rotational motion Kinematics of rotnl motion Dynamics of rotnl motion Rotnl Analogue of mass Angular Displacement, -s/r Angular Velocity, a) dg/dt Angular Acceleration, d)/dt Equations of rotational motion Angular Momentunm Moment of Inertia For a rigid body, l-) mir, Perpendicular Axis theorem . Parallel Axis theorem Of particle about a point: . . Of a rigid body rotating about a . fixed axis: of of + 2 From Newton's 2nd law, Text dL/dt Torque about the axis of rotation: Work done by torque, W Power, P- Conservation of Angular Momentum : Itext-0, then dt = 0, so that L = la) is constant 0, then0, so that LIo is constant
Pure rolling motion : For a body rolling without slipping, velocity of centre of mass, Vcm rw. Kinetic energv, K - K+KR-mv?m(1 + C) When a force acts on a body Snapshot of rolling motion On an inclined plane A force P is applied at a distance For rigid bodies: Solid cylinder, hollow Arigid bedy of radius R, mass M and moment of inertia, I kMR2 is released at rest. above the centre of a rigid body of radius R, mass M and moment of inertia kMR2 about an axis passing through the centre of mass cylinder, solid sphere and hollow sphere. . Order of acceleration ass asc ahs ahc . Order of required friction for pure 1+ where C F(R x) F(x- kR) rolling These both hold for f smg Order of required minimum friction coefficient for pure rolling cm mgsine
Combined translation and rotational motion : If all the points in the body rotates about an axis of rotation and the axis of rotation moves with respect to the ground. The speed of a point on the circumference at any instant t is Velocity of any point of the rigid body in combined motion is the vector sum of v and x and y coordinates of the bottommost point at any time t, (x, y) (vt-rsinot,r -rcosot) Angular momentum of a rigid body in combined motion: CM 0 vo
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