Rotational Dynamics Concepts

   Tuesday, July 21, 2020   

Rotational Dynamics Concepts include all Definitions, Laws, Diagrams, Rules, Examples, Results etc.

Page 1

Rigid Body | Instantaneous angular velocity of rigid body | Angular velocity of a rigid body from linear velocity of two points | No-slip condition of string on pulley | Relation Between Angular Velocity and Linear Velocity | Relation between frequency, time period and angular velocity | Radius of Gyration | Real life examples of moment of inertia | Define Moment of inertia | Physical Significance of Moment of inertia

Page 2

Moment of inertia of a system of discrete particles | Moment of inertia of continuous bodies | Moment of inertia of disc, ring and cylinder | Moment of inertia of shell and sphere | Example of moment of inertia of variable mass density | Superposition Principle to find moment of inertia of composite bodies | Perpendicular Axis Theorem | Parallel Axis Theorem | Perpendicular and Parallel Axis Theorem | Moment of Inertia of rod

Page 3

Moment of inertia of a rectangular plate | Masses attached to fixed pulleys with given moment of inertia | Masses attached to multiple fixed pulleys with defined moment of inertia | Clockwise and Anticlockwise Moments | Units of Moment of Force | Moment of Force or Torque | Net torque due to internal forces equals zero for a rigid body | Equation of torque about point of projection for a projectile

Page 4

Couple | Principle of Moments | Factors Affecting Turning of a Body | Examples of turning effect of force | Principle of Moments | Condition for rotational equilibrium | Discuss the condition for rotational and translational equilibrium | Problem on total equilibrium in which all the forces are not coplanar

Page 5

Problems on total equilibrium involving friction where line of action of normal force changes | Pure Rotational motion | Rotation plus Translation motion | Examples of Rolling motion | Pure Transnational motion | Precession | Angular Velocity of a rigid body | Torque about an axis for a point object

Page 6

Torque about an axis for a rigid body | Angular momentum in terms of angular velocity | Relation between rate of change on angular momentum with net torque | Angular Momentum | Angular Momentum of a particle with defined trajectory | Angular Momentum and its relation with Energy | Angular momentum of a rigid body about an axis through its center of mass | Angular momentum of a rigid body about an axis other than its center of mass

Page 7

Areal velocity of a point object | Conservation of Angular Momentum | Conservation of Angular Momentum | Relation between rate of change on angular momentum with net torque on a system of particles | Numerical to find moment of force (torque) | Problem on fixed axis rotation with constant angular velocity | Conservation of Angular Momentum | Application of conservation of angular momentum of a rigid body about a fixed axis

Page 8

Conservation of Angular Momentum of more than one rigid body | Conservation of Angular Momentum incorporating relative motion between bodies | Torque equations in reference frame of axis | Work Done by torque | Power delivered by torque | Fixed axis rotation with constant torque for rigid bodies | Kinetic Energy in rotation plus translation | Total velocity and acceleration of a point in rigid body in rotation plus translation

Page 9

Comparison of quantities in rotational and translational motion | Problem on rotation plus translation where more than one force contributes to torque | Instantaneous axis of rotation | Instantaneous axis of rotation to find angular velocity | Pure rolling and its conditions | Use of formula of kinetic energy of a body in pure rotation | Problem on Rolling Friction | Conditions on coefficient of friction to facilitate pure rolling

Page 10

Relationship between angular acceleration and linear acceleration | Condition of slipping to determine nature of slipping | Condition of slipping to determine direction of friction | No-slip condition where multiple points of contact are involved in pure rolling | Conservation of energy equation for rigid bodies performing pure rolling where centre of mass moves in vertical circle | Force equations for rigid bodies performing pure rolling where centre of mass moves in a vertical circle | Force and torque equations about different axes for pure rolling | Condition for breaking off from surface in case of objects performing pure rolling on a curved surface

Page 11

Velocity of the ring rolling down the inclined plane | Velocity of disc rolling down the inclined plane | Velocity of sphere rolling down the inclined plane | Problems on rolling where more than one force contributes to torque | Pure rolling using angular momentun conservation about point of contact | Energy conservation in pure rolling | Impulsive Hinge Force | Angular Impulse

Page 12

Problems on collisions of rigid bodies using angular impulse relations | Condition of toppling | Use instantaneous axis of rotation to find condition of total equilibrium | Condition for toppling | Solve Problem on instantaneous axis of rotation