Physics 2 (Grade 11)
Gravitation, rotation, momentum, work, energy and thermal energy.
Gravitation, rotation, momentum, work, energy and thermal energy.
Units of the book
| Unit | What to know |
|---|---|
| Gravitation | Kepler’s laws, universal gravitation |
| Rotational motion | angular displacement and velocity, torque, equilibrium |
| Momentum | impulse, conservation in collisions |
| Work, energy and machines | work, power, mechanical advantage and efficiency |
| Energy | kinetic and potential energy, conservation |
| Thermal energy | temperature, specific heat, changes of state, the laws of thermodynamics |
Formulas to remember
- F = G m₁m₂ / r²: universal gravitation
- τ = F r sin θ: torque
- v = rω: linear speed
- p = mv: momentum
- FΔt = Δp: impulse
- W = Fd cos θ: work
- P = W/t: power
- KE = ½mv²: kinetic energy
- PE = mgh: potential energy
- Q = mcΔT: heat
- K = °C + 273: kelvin
- ΔU = Q − W: first law of thermodynamics
🧠 Memory kit: gravity, rotation, momentum, energy and heat
| Formula | In plain words | How to remember it |
|---|---|---|
| F = G m₁m₂ / r² | Universal gravitation. G = 6.67 × 10⁻¹¹ N·m²/kg². | Inverse square: double the distance → a quarter of the force, triple → a ninth. |
| g = GM / r² | Gravity at the surface of a planet of mass M and radius r. | It is the gravitation law divided by the small mass. |
| v = √(GM / r) | Speed of a satellite in a circular orbit. | A farther orbit is slower. |
| T² ∝ r³ | Kepler’s third law: period squared is proportional to orbit radius cubed. | “2 for time, 3 for distance.” |
| v = rω, ω = Δθ / Δt | Linear speed = radius × angular speed (rad/s). | On a roundabout, the rider at the edge goes faster though both turn together. |
| τ = F r sinθ | Torque: the turning effect of a force. | That is why door handles are far from the hinges: bigger r → more torque. |
| ΣF = 0, Στ = 0 | The two conditions for equilibrium: no sliding and no turning. | For a balanced seesaw: F₁r₁ = F₂r₂. |
| p = mv | Momentum = mass × velocity (kg·m/s). | A slow truck can have more momentum than a fast car. |
| FΔt = Δp | Impulse = force × time = change in momentum. | An airbag makes the time longer, so the force is smaller for the same impulse. |
| m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′ | Momentum is conserved in collisions and explosions (closed system). | If they stick: (m₁ + m₂)v′. A gun recoils because total momentum stays zero. |
| W = Fd cosθ | Work (joules). Zero when the force is perpendicular to the motion. | Carrying a bag while walking level: the lifting force does zero work (θ = 90°). |
| P = W / t = Fv | Power: how fast work is done (watts). 1 hp = 746 W. | Running or walking up stairs: same work, different power. |
| MA = F r / F e, IMA = d e / d r | Actual mechanical advantage (forces) and ideal (distances). | A machine saves force by costing distance. |
| e = (MA / IMA) × 100% = (W out / W in) × 100% | Efficiency, always below 100% in real machines. | “What comes out ÷ what goes in.” |
| KE = ½mv² | Kinetic energy. | Double the speed → four times the energy (speed is squared). |
| PE = mgh, PE s = ½kx² | Gravitational and elastic potential energy. | mgh = weight × height. |
| KE + PE = ثابت ⇒ v = √(2gh) | Mechanical energy is conserved without friction; speed after falling h. | From mgh = ½mv² the mass cancels: heavy and light land at the same speed. |
| K = °C + 273 | Celsius to kelvin. Absolute zero = 0 K = −273 °C. | A change of 1 K equals a change of 1 °C. |
| Q = mcΔT | Heat to change temperature. c of water = 4180 J/kg·K. | Say it “m-c-at”. |
| Q = mL | Latent heat for a change of state (melting H f or boiling H v) with no change in temperature. | While boiling the temperature stays put: the energy breaks bonds. |
| ΔU = Q − W | First law: change in internal energy = heat added − work done by the system. | Like a bank account: Q is a deposit, W a withdrawal. |
- Kepler’s three laws: (1) orbits are ellipses with the Sun at a focus, (2) equal areas in equal times (faster near the Sun), (3) T² ∝ r³. Remember: “shape, speed, time”.
- Second law of thermodynamics: heat flows by itself only from hot to cold, and entropy (disorder) increases. No engine is 100% efficient.
- Elastic vs inelastic: momentum is always conserved; kinetic energy only in elastic collisions.
A way of memorizing that sticks
- Understand before you memorize: read “in plain words” for each formula and say out loud what it measures and why each quantity is multiplied or divided. A formula you understand takes a minute to learn.
- Active recall: cover the formula column and write it from memory, then check. Writing from memory beats rereading by far.
- Spaced repetition: review the same sheet after 1 day, 3 days, a week and two weeks. Four short reviews lock it in until test day.
- Your own formula page: write every formula of a book on one page by hand. If it does not fit, you are writing things you can derive, so cut them.
- Teach it: explain the formula to a friend, or to yourself in a mirror, in two sentences. If you cannot explain it, you do not know it yet.
- Use it at once: after each group, press “Try one” in the patterns below. Memory sets when you use it.
Question patterns
Gravitation and Kepler
Doubling the distance divides the force by 4. A planet is fastest nearest the Sun.
Rotation, torque and balance
Balance: m₁d₁ = m₂d₂. The minute hand turns 2π each hour.
Momentum and collisions
Momentum before = momentum after. Sticking together: v = m₁v₁/(m₁ + m₂).
Work, power and machines
A force perpendicular to motion does no work. Efficiency = MA ÷ IMA.
Energy
Doubling speed quadruples kinetic energy. Falling: v = √(2gh).
Thermal energy
A change in °C equals the change in K. Heat flows from hot to cold.
- Gas laws need kelvin, but ΔT in Q = mcΔT works in °C.
- Work is zero at 90°.
More patterns (figures and calculations)
Angular displacement and velocity
ω = 2π/T, v = rω
Impulse, energy and power
FΔt = mΔv, E = Pt
Lifting work
W = mgh