Complete Physics Revision: Kinematics, Laws - JEE Physics

Complete Physics Revision: Kinematics, Laws of Motion, Friction, Work, Energy, Rotation, and Thermal Physics

Kinematics: 1D and 2D Motion

Kinematics covers the motion of particles in one and two dimensions, focusing on displacement, velocity, acceleration, and the relationships between them. Key concepts include the distinction between distance and displacement, and the use of calculus for non-uniform motion.

• Displacement: Change in position vector, $r_{final} - r_{initial}$
• Distance: Actual path length traveled
• Average speed: Total distance / total time
• Average velocity: Total displacement / total time
• Average acceleration: Change in velocity / total time -…

Complete Physics Revision: Kinematics, Laws of Motion, Friction, Work, Energy, Rotation, and Thermal Physics

Kinematics: 1D and 2D Motion

Kinematics covers the motion of particles in one and two dimensions, focusing on displacement, velocity, acceleration, and the relationships between them. Key concepts include the distinction between distance and displacement, and the use of calculus for non-uniform motion.

• Displacement: Change in position vector, $r_{final} - r_{initial}$
• Distance: Actual path length traveled
• Average speed: Total distance / total time
• Average velocity: Total displacement / total time
• Average acceleration: Change in velocity / total time
• Differentiation: Position to velocity, velocity to acceleration
• Integration: Acceleration to velocity, velocity to position

Key Equations (for constant acceleration):

• $v = u + at$
• $s = ut + \frac{1}{2}at^2$
• $v^2 = u^2 + 2as$
• $s_n = u + \frac{a}{2}(2n-1)$ (displacement in the $n$th second)

Graphical Interpretations:

• Area under $a$-$t$ graph: Change in velocity
• Area under $v$-$t$ graph: Displacement
• Slope of $x$-$t$ graph: Velocity
• Slope of $v$-$t$ graph: Acceleration

Projectile and Relative Motion

Projectile motion involves two-dimensional motion under gravity, with independent analysis along $x$ and $y$ axes. Relative motion problems often involve river-boat and rain-man scenarios.

• Projectile equations:
  • Time of flight: $T = \frac{2u_y}{g}$
  • Range: $R = \frac{u^2 \sin 2\theta}{g}$
  • Maximum height: $H = \frac{u^2 \sin^2\theta}{2g}$
  • Equation of trajectory: $y = x \tan\theta - \frac{gx^2}{2u^2 \cos^2\theta}$
• Relative velocity: $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$
• River-boat problems:
  • Minimum time: $t_{min} = \frac{d}{v_{man}}$
  • Minimum distance: $t = \frac{d}{v_{man} \cos\theta}$

Graphical and Multi-Stage Motion Analysis

Multi-stage motion and graphical methods are essential for analyzing journeys with changing acceleration or velocity.

• Multi-stage motion: Use area under $v$-$t$ or $a$-$t$ graphs for each segment
• Key result for constant acceleration from rest: Distances in successive seconds are in the ratio $1:3:5:7...$
• Tap water problem: Droplets at regular intervals, use $1:3:5...$ ratios for positions

Laws of Motion and Free Body Diagrams

Newton’s Laws govern the dynamics of particles and systems. Free body diagrams (FBDs) are crucial for visualizing forces.

• Newton’s Second Law: $F = dp/dt$
• FBD rules:
  • $mg$ always downwards
  • Normal force perpendicular to surface
  • Tension away from the body
  • For pulleys: $a = (F_{pull} - F_{resist})/M_{total}$
• Spring force: $F = kx$
• Pseudo force: $F_{pseudo} = m a_{frame}$ (for non-inertial frames)

Friction: Static, Kinetic, and Rolling

Friction opposes relative motion and is classified as static or kinetic. Rolling friction involves both translation and rotation.

• Static friction: $f_s \leq \mu_s N$
• Kinetic friction: $f_k = \mu_k N$
• Maximum static friction: $f_{max} = \mu_s N$
• Rolling friction: Always static in pure rolling
• Minimum force to move block:
  • Horizontal: $F_{min} = \mu mg$
  • At angle: $F_{min} = \frac{\mu mg}{\sqrt{1+\mu^2}}$
• Inclined plane:
  • $a = g(\sin\theta - \mu \cos\theta)$ (down the plane)
  • $a = g(\sin\theta + \mu \cos\theta)$ (up the plane)

Work, Power, and Energy

Work-energy principles relate force, displacement, and energy changes. Power quantifies the rate of energy transfer.

• Work done: $W = \int \vec{F} \cdot d\vec{x}$
• Work by spring: $W = -\frac{1}{2}k(x_f^2 - x_i^2)$
• Work-energy theorem: $W_{net} = \Delta KE$
• Power: $P = \vec{F} \cdot \vec{v}$
• Stopping distance: $x = \frac{u^2}{2a}$ (for constant $a$)
• Conservation of mechanical energy: $KE + PE = \text{constant}$ (if only conservative forces)

Rotation and Rolling Motion

Rotational dynamics involve torque, angular momentum, and moment of inertia. Rolling combines translation and rotation.

• Moment of inertia (I): Depends on mass distribution; for a disc about center, $I = \frac{1}{2}mr^2$
• Parallel axis theorem: $I = I_{cm} + Md^2$
• Perpendicular axis theorem: $I_z = I_x + I_y$
• Torque: $\tau = I\alpha$
• Angular momentum: $L = I\omega$
• Rolling without slipping: $v = r\omega$
• Acceleration on incline (rolling): $a = \frac{g \sin\theta}{1 + \frac{I}{mr^2}}$
• Energy in rolling: $KE_{total} = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$

Collisions and Center of Mass

Collisions are analyzed using conservation of momentum and, for elastic collisions, kinetic energy. Center of mass (COM) is the weighted average position of mass.

• COM for discrete particles: $x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$
• COM for continuous bodies: $x_{cm} = \frac{\int x\,dm}{\int dm}$
• Momentum conservation: $\sum m_i v_{i,initial} = \sum m_i v_{i,final}$
• Elastic collision: Both momentum and kinetic energy conserved
• Inelastic collision: Only momentum conserved
• Coefficient of restitution: $e = \frac{v_2 - v_1}{u_1 - u_2}$
• Kinetic energy loss (inelastic): $\Delta KE = \frac{1}{2}\mu (u_1 - u_2)^2 (1 - e^2)$

Thermal Expansion and Calorimetry

Thermal expansion describes how materials change size with temperature. Calorimetry deals with heat transfer and phase changes.

• Linear expansion: $\Delta L = L_0 \alpha \Delta T$
• Area expansion: $\Delta A = A_0 \beta \Delta T$
• Volume expansion: $\Delta V = V_0 \gamma \Delta T$
• Heat required (no phase change): $Q = ms\Delta T$
• Heat for phase change: $Q = mL$
• Water equivalent: $W = m_{body} s_{body}$
• Apparent expansion: $\gamma_{apparent} = \gamma_{liquid} - 3\alpha_{container}$

Heat Transfer: Conduction and Radiation

Heat transfer occurs via conduction, convection, and radiation. In conduction, heat flows through a material; in radiation, energy is emitted as electromagnetic waves.

• Conduction (steady state): $Q/t = \frac{KA \Delta T}{L}$
• Thermal resistance: $R = \frac{L}{KA}$
• Series/parallel analogy: Use resistances for composite rods
• Radiation (Stefan-Boltzmann law): $P = eA\sigma (T^4 - T_s^4)$
• Net heat exchange: $P_{net} = eA\sigma (T^4 - T_s^4)$
• Wien’s displacement law: $\lambda_{max} T = \text{constant}$

Key Problem-Solving Strategies and Pitfalls

Physics problems often require careful attention to conditions, correct application of formulas, and awareness of common traps.

• Check for constant acceleration: Use kinematic equations only if $a$ is constant

• Graph interpretation: Always check axes and what area/slope represents

• Friction direction: In rolling, friction is static and direction depends on motion

• Work by friction: For rolling without slipping, static friction does no net work

• Collision type: Confirm if collision is elastic or inelastic before applying energy conservation

• Thermal expansion: For composite rods, consider constraints and relative expansion

• Heat transfer: In steady state, heat current is same through all series elements

• Radiation: Use net power for temperature change, not just emission or absorption alone

• Always verify units and conversions, especially in thermal and heat transfer problems.

• For multi-stage or composite systems, break into segments and apply conservation laws or formulas to each.

• In exam settings, use elimination and estimation when options allow, but always check for hidden conditions or exceptions.