Physics Exam Master Sheet: Momentum, Energy, Rotational Motion, Gravity, Projectiles, Solids

Chapter 6 – Momentum & Impulse

Momentum

Momentum is a fundamental concept in physics describing the quantity of motion an object possesses. It is a vector quantity, meaning it has both magnitude and direction.

• Definition: Momentum (p) is the product of mass and velocity.

• Formula: $p = mv$

• Units: kg·m/s

• Type: Vector

• Example: A 2 kg ball moving at 3 m/s has momentum $p = 2 \times 3 = 6$ kg·m/s.

Impulse

Impulse quantifies the effect of a force acting over a period of time, resulting in a change in momentum.

• Definition: Impulse (J) is the product of force and the time interval during which it acts.

• Formula: $J = F\Delta t = \Delta p$

• Units: N·s

• Type: Vector

• Example: A force of 10 N applied for 2 s gives impulse $J = 10 \times 2 = 20$ N·s.

Conservation of Momentum

In the absence of external forces, the total momentum of a system remains constant.

• Elastic Collisions: Both kinetic energy and momentum are conserved.

• Inelastic Collisions: Only momentum is conserved; kinetic energy is not.

• Newton’s Second Law: Relates force to the rate of change of momentum.

• Newton’s Third Law: Explains equal and opposite impulses during interactions.

Chapter 7 – Work & Energy

Work

Work is the process of energy transfer when a force acts upon an object to cause displacement.

• Formula: $W = Fd \cos\theta$

• Units: Joules (J)

• Type: Scalar

• Positive Work: Force and displacement in same direction.

• Negative Work: Force and displacement in opposite directions.

• Zero Work: Force perpendicular to displacement.

Power

Power measures the rate at which work is done or energy is transferred.

• Formula: $P = \frac{W}{t}$

• Units: Watts (W)

• Type: Scalar

Kinetic and Potential Energy

• Kinetic Energy (KE): Energy due to motion. $KE = \frac{1}{2}mv^2$

• Potential Energy (PE): Energy due to position. $PE = mgh$

• Elastic Potential Energy: $PE_{elastic} = \frac{1}{2}kx^2$

• Hooke’s Law: $F = kx$ (force required to stretch/compress a spring)

Work-Energy Theorem & Conservation

• Work-Energy Theorem: $W_{net} = \Delta KE$

• Conservation of Energy: Total energy remains constant if no non-conservative forces (like friction) act.

Chapter 8 – Rotational Motion

Angular Quantities

Rotational motion involves angular displacement, velocity, and acceleration.

• 1 revolution: $2\pi$ radians = 360°

• Angular velocity: $\omega = \frac{\Delta \theta}{\Delta t}$

• Angular acceleration: $\alpha = \frac{\Delta \omega}{\Delta t}$

• Linear velocity: $v = r\omega$

Centripetal Motion

• Centripetal acceleration: $a_c = \frac{v^2}{r}$

• Centripetal force: $F_c = \frac{mv^2}{r}$ (directed toward center)

Torque & Rotational Inertia

• Torque: $\tau = rF \sin\theta$ (causes rotation)

• Rotational inertia: $I = \sum mr^2$ (resistance to rotational acceleration)

Angular Momentum

• Angular momentum: $L = I\omega$

• Conservation: Angular momentum is conserved in absence of external torque.

Chapter 9 – Gravity

Universal Gravitation

Gravity is a fundamental force of attraction between masses.

• Newton’s Law of Universal Gravitation: $F = G\frac{m_1 m_2}{r^2}$

• Gravitational constant: $G = 6.67 \times 10^{-11}$ N·m²/kg²

• Gravity is always attractive.

Weight and Gravitational Field

• Acceleration due to gravity: $g = 9.8$ m/s²

• Weight: $W = mg$

• Gravitational field: Measured in N/kg

Tides

• Spring tides: Occur when Sun, Moon, and Earth align (strongest tides).

• Neap tides: Occur when Sun and Moon are at right angles to Earth (weakest tides).

Chapter 10 – Projectile & Orbits

Projectile Motion

Projectile motion describes the path of an object launched into the air, subject to gravity.

• Horizontal velocity: Constant (no horizontal acceleration)

• Vertical acceleration: $g$ downward

Orbital Motion

• Circular orbit: Kinetic and potential energy are constant.

• Elliptical orbit: KE and PE vary, but total energy remains constant.

• Escape velocity (Earth): $\approx 11.2$ km/s

Kepler’s Laws

• First Law: Orbits are ellipses.

• Second Law: Equal areas swept in equal times.

• Third Law: $T^2 \propto r^3$ (orbital period squared proportional to radius cubed)

Elasticity

• Hooke’s Law: $F = kx$

• Tension: Stretches material.

• Compression: Squeezes material.

Key Formula Table

The following table summarizes key physical quantities, their formulas, units, and whether they are scalar or vector quantities.

Quantity	Formula	Units	Type
Momentum	$p = mv$	kg·m/s	Vector
Impulse	$J = F\Delta t$	N·s	Vector
Work	$W = Fd \cos\theta$	J	Scalar
Power	$P = \frac{W}{t}$	W	Scalar
Kinetic Energy	$\frac{1}{2}mv^2$	J	Scalar
Potential Energy	$mgh$	J	Scalar
Centripetal Force	$\frac{mv^2}{r}$	N	Vector
Torque	$rF \sin\theta$	N·m	Vector
Angular Momentum	$I\omega$	kg·m²/s	Vector
Gravitational Force	$G\frac{m_1 m_2}{r^2}$	N	Vector
Density	$\frac{m}{V}$	kg/m³	Scalar