Lecture 77 of 100Week9 Lectures
Rigid body motion XVII – A review of the relation between angular momentum and angular velocity, moment of inertia tensor and the principal axes Edit Lesson
Prof. Manoj Harbola · IIT Kanpur
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- Introduction to Vectors
- Addition and subtraction of vectors
- Multiplying vectors
- Introduction to vectors: solved examples I
- Transformation of vectors under rotation
- Vector products and their geometric interpretation
- Vector Product: Kronecker Delta and Levi-Civita symbols-I
- Vector Product: Kronecker Delta and Levi-Civita symbols-II
- Introduction to vectors: solved examples II
- Equilibrium of rigid bodies – Forces and torques
- Calculating torques and couple moments-I
- Calculating torques and couple moments-II
- Finding a force and a couple equivalent to an applied force
- Different elements and associated forces and torques-I
- Different elements and associated forces and torques - II
- Solved examples; equilibrium of bodies – I
- Solved examples; equilibrium of bodies – II
- Forces in different geometric configuration
- Plane trusses I - building a truss and condition for it to be statically determinate
- Plane trusses II - calculating forces in a simple truss and different types of trusses
- Plane trusses III - calculating forces in a simple truss by method of joints
- Plane trusses IV- Solved examples for calculating forces in a simple truss by method of joints
- Plane trusses V - Solved examples for calculating forces in a simple truss by method of joints
- Plane trusses VI: method of sections for calculating forces in a simple truss
- Dry friction I - introduction with an example
- Dry friction II - a solved example
- Dry friction III - Dry thrust bearing and belt friction with demonstration
- Dry friction IV - Screw friction and rolling friction
- Dry friction V: Solved examples
- Properties of plane surfaces I - First moment and centroid of an area
- Properties of plane surfaces II - Centroid of an area made by joining several plane surfaces
- Properties of plane surfaces III - Centroid of a distributed force and its relation with centre of gravity
- Properties of plane surfaces IV - solved examples of calculation of first moment and centroid of distributed forces
- Properties of plane surfaces V- Second moment and product of an area and radius of gyration
- Properties of plane surfaces VI - Parallel axis transfer theorem for second moment and product of an area
- Properties of plane surfaces VII - transformation of second moment and product of an area under rotation of coordinate axes
- Properties of plane surfaces VIII - second moment and product of an area, solved examples
- Method of virtual work I - degrees of freedom, constraints and constraint forces
- Method of virtual work II - virtual displacement, virtual work and equilibrium condition in terms of virtual work
- Method of virtual work III - solved examples
- Motion of a particle in a plane in terms of planar polar coordinates
- Planar polar coordinates: solved examples
- Description of motion in cylindrical and spherical coordinate systems
- Using planar polar, cylindrical and spherical coordinate systems: solved examples
- Motion with constraints, constraint forces and free body diagram
- Motion with constraints – solved examples
- Motion with dry friction – solved examples
- Motion with drag – solved examples
- Equation of motion in terms of linear momentum and the principle of conservation of linear momentum
- Linear momentum and centre of mass
- Momentum transfer, impulse and force due to a stream of particles hitting an object
- Momentum and the variable mass problem
- Linear momentum – solved examples
- Work and energy I - work energy theorem; conservative and non-conservative force fields
- Work and energy II - Definition of potential energy for conservative forces; total mechanical energy and the principle of conservation of energy
- Work and energy III - Two solved examples using conservation principles
- Work and energy IV – Further discussion on potential energy
- Work and energy V - Solved examples
- Work and energy VI – Applying conservation principles to solve a collision problem
- Work and energy VII - Solved examples
- Rigid body motion I - degrees of freedom and number of variables required to describe motion of a rigid body
- Rigid body motion II - Equation of motion for a single particle in terms of angular momentum and torque; motion of a conical pendulum
- Rigid body motion III - Conservation of angular momentum; angular momentum for a collection of particles
- Rigid body motion IV - applying angular momentum conservation, a solved example
- Rigid body motion V (fixed axis rotation) - some demonstrations of conservation of angular momentum about fixed axis
- Rigid body motion VI (fixed axis rotation) - Some more demonstrations and related problems
- Rigid body motion VII (fixed axis rotation) - Kinetic energy and moment of inertia for fixed axis rotation and some solved examples
- Rigid body motion VIII (fixed axis rotation) - solved examples for calculating moment of inertia and conservation of angular momentum
- Rigid body motion –IX (fixed axis rotation): solved examples
- Rigid body motion X - rotation and translation with axis moving parallel to itself
- Rigid body motion XI - solved examples for rotation and translation with axis moving parallel to itself
- Rigid-body dynamics XII - Some demonstrations on general motion of rigid bodies
- Rigid-body dynamics XIII - Infinitesimal angles as vector quantities and change of a vector when rotated by an infinitesimal angle
- Rigid-body dynamics XIV - Angular velocity and the rate of change of a rotating vector; relating change in angular velocity to an applied torque
- Rigid-body dynamics XV - Relationship between angular momentum and angular velocity – the moment of inertia tensor and the principal axes
- Rigid-body dynamics XVI: Solved examples
- Rigid body motion XVII – A review of the relation between angular momentum and angular velocity, moment of inertia tensor and the principal axes Edit Lesson
- Rigid body motion XVIII- Solved examples for calculating rate of change of angular momentum and torque when angular velocity and angular momentum are not parallel
- Rigid body dynamics XIX: understanding demonstrations shown earlier using equation of motion
- Rigid body dynamics XX - understanding demonstrations shown earlier using equation of motion (Euler equations)
- Rigid body dynamics XXI - Euler equations, solved examples
- Simple harmonic motion I - expanding potential energy about the equilibrium point and the corresponding force
- Simple harmonic motion II : solving the equation of motion with given initial conditions
- Simple harmonic motion III - solved examples
- Simple harmonic motion IV - representing simple harmonic motion on a phasor diagram; energy of an oscillator
- Simple harmonic motion V- solved examples
- Simple harmonic motion VI - solving the equation of motion with constant friction in the system
- Simple harmonic motion VII - harmonic oscillator with velocity-dependent damping (heavy damping)
- Simple harmonic motion VIII - harmonic oscillator with velocity-dependent damping (critical damping)
- Simple harmonic motion IX- solved examples
- Simple harmonic motion X- harmonic oscillator with velocity-dependent damping (light damping)
- Simple harmonic motion XI- solved examples
- Simple harmonic motion XII - oscillations of an un-damped harmonic oscillator subjected to an oscillatory force
- Simple harmonic motion XIII - oscillations of a forced damped harmonic oscillator I
- Simple harmonic oscillator XIV: oscillations of a forced damped harmonic oscillator II
- Simple harmonic oscillator XV: Energy and power in a forced damped harmonic oscillator
- Simple harmonic oscillator XVI: Solved examples
- Equation of motion in a uniformly accelerating frame
- Motion described in a uniformly accelerating frame; solved examples -I
- Motion described in a uniformly accelerating frame; solved examples -II