Introduction - Center Of Mass - System Of Particles And Rotational Motion

Laws Of Motion:

NCERT 11th Physics, Ch 5- Laws of Motion

• Newton’s First Law: Inertia- objects tend to resist changes in their motion.
• Newton’s Second Law: Force = rate of change of momentum -> F = dp/dt = m(dv/dt)
  • Impulse: Force acts over a short duration, causing a change in momentum = J=Ft
• Newton’s Third Law: Every action has an equal and opposite reaction.
• Understanding resultant forces, forces of friction, tension and equilibrium.
• Applications of Newton’s Laws in motion on an inclined plane, motion in a vertical circle and projectile motion.

Center Of Mass:

NCERT 11th Physics, Ch 8 - Gravitation NCERT 12th Physics, Ch 1- Electric Charges and Fields

• Centre of mass (CM): The point where the total mass of the system seems to be concentrated = Σ(mi*ri)/M
• CM for regular objects like a rod, ring, sphere etc.
• Motion of the center of mass is the same as the motion that would be produced by a single particle with the total mass of the system at the center of mass.
• Finding CM experimentally
• CM of composite objects and continuous mass distributions.
• Applications in describing the motion of planets, projectiles, and other objects.

System Of Particles:

NCERT 11th Physics, Ch 9 - Mechanical properties of solids and fluids NCERT 11th Physics, Ch 10- Thermal properties of matter NCERT 12th Physics, Ch 15 - Communication Systems NCERT 12th Physics, Ch 6 - Work, Energy, and Power

• Momentum: Quantity that describes the motion of the object and is a vector quantity = P=mv
• Linear Momentum: Total momentum of a system remains constant in absence of external forces = ∑P = constant
• Angular Momentum: rotational analogue of linear momentum = L = Iω
• Understanding Conservation of linear and angular momentum and its applications in the motion of objects and collisions (elastic and inelastic).
• Collisions: Impulse-momentum relationship, conservation of momentum and coefficient of restitution.
• Rocket Propulsion and its working principle based on conservation of momentum.

Rotational Dynamics:

NCERT 12th Physics, Ch 14- Semiconductor Electronics:

• Angular Displacement: Change in angular position of an object relative to a fixed reference point
• Angular velocity: Rate of change of angular displacement = ω = dθ/dt
• Angular acceleration: Rate of change of angular velocity = α = dω/dt
• Rotational kinematics equations: analogous to linear motion equations.
• Moment of inertia: Resistance of an object to rotational motion = I= ∑mr2
• Calculation of moment of inertia for various shapes and objects using integration.
• Finding rotational kinetic energy: K=1/2 Iω2
• Torque: Rotational analogue of force =τ = Iα

Moment Of Inertia:

NCERT 12th Physics, Ch 14 -Semiconductor Electronics

• Understanding moment of inertia (I) as a measure of an object’s resistance to angular acceleration.
• Moment of inertia depends on mass distribution and axis of rotation.
• Parallel Axis Theorem: Moment of inertia about any axis is equal to the sum of moment of inertia about a parallel axis passing through the center of mass and the product of total mass and the square of the distance between the two axes.
• Moment of inertia for simple bodies like a ring, sphere, rod etc.
• Applications in analyzing rotational motion of objects, such as compound pendulums and physical pendulums.

Rolling Motion:

NCERT 12th Physics, Ch 13- Nuclei

• Rolling without slipping condition: v = ωR
• Translational and rotational kinetic energy in rolling motion
• Conservation of energy and its application in rolling objects.
• Work done in rolling motion due to friction.

Rotational Equilibrium:

• Conditions for rotational equilibrium: Net torque acting on the object is zero.
• Objects in equilibrium have a stationary center of mass.
• Applications in analyzing stability and equilibrium of structures and machines.

Recommended Readings and Resources

• Resnick Halliday Krane Physics, Volume 1
• University Physics by Young and Freedman
• Fundamentals of Physics by Halliday Resnick and Walker
• Concepts of Physics by H C Verma
• NCERT exemplar problems and previous years’ JEE question papers.