AP Physics 1 equation sheet, explained

By Ashraf Bhura, Co-Founder, STEM-Tutor · Updated October 2026

You get an equation sheet in the AP Physics 1 exam, but it only helps if you know what each equation means and when it applies. Here is the sheet explained topic by topic.

What the equation sheet is for

The College Board provides an equation sheet in the exam, so you do not need to memorise formulas. The sheet does not tell you which equation to use. That decision is what the exam is really testing. You can download the current official sheet from AP Central; the layout is updated from time to time.

Kinematics

• v = v₀ + at: velocity after time t at constant acceleration.
• x = x₀ + v₀t + ½at²: position after time t at constant acceleration.
• v² = v₀² + 2a(x − x₀): links speed and displacement when time is unknown.

All three only work when acceleration is constant. If the acceleration changes, use graphs instead: the slope of a velocity-time graph is acceleration and the area under it is displacement.

Forces and circular motion

• ΣF = ma: the net force, not any single force, causes acceleration.
• F_f ≤ μF_N: static friction can be anything up to μF_N; kinetic friction equals μF_N.
• F_s = −kΔx: spring force grows with stretch and points back toward equilibrium.
• a_c = v²/r: centripetal acceleration points toward the centre of the circle.
• F_g = Gm₁m₂/r²: gravitational force between two masses.

Energy and power

• K = ½mv²: kinetic energy.
• ΔU_g = mgΔy: change in gravitational potential energy near Earth's surface.
• U_s = ½kΔx²: energy stored in a spring.
• W = Fd cosθ: work done by a constant force.
• P = ΔE/Δt: power is the rate of energy transfer.

Momentum

• p = mv: momentum is a vector, so direction matters.
• J = FΔt = Δp: impulse equals the change in momentum.

Momentum is conserved when there is no net external force on the system. Kinetic energy is only conserved in elastic collisions.

Rotation

• τ = rF sinθ: torque depends on the force and how far from the axis it acts.
• Στ = Iα: the rotational version of Newton's second law.
• L = Iω and K = ½Iω²: angular momentum and rotational kinetic energy.

Oscillations and fluids

• T_s = 2π√(m/k) and T_p = 2π√(L/g): periods of a mass on a spring and a simple pendulum.
• ρ = m/V, P = F/A and P = P₀ + ρgh: density and pressure in fluids.
• F_b = ρVg: buoyant force equals the weight of fluid displaced.
• A₁v₁ = A₂v₂: fluid speeds up where a pipe narrows.

How to use the sheet well

1. Decide the principle first: forces, energy or momentum. Then find the equation.
2. Check the conditions, such as constant acceleration or no external force.
3. In free-response questions, write the starting equation before substituting. It earns marks.
4. Practise with the sheet beside you all year, so you know exactly where everything is.

Finally, practise reading the sheet's notation: subscripts, vector symbols and units are given in a specific style, and recognising them instantly saves time in the exam.

Worked examples, one per topic

Example 1: a block on a slope

A 2 kg block slides down a 30° slope. Find its acceleration with no friction, then with μ_k = 0.2. Use g = 9.8 m/s².

• Along the slope, the driving force is mg sinθ, so without friction a = g sin30° = 4.9 m/s².
• With friction, F_N = mg cosθ and friction = μ_kF_N. So a = g(sin30° − 0.2 cos30°) = 9.8(0.5 − 0.173) ≈ 3.2 m/s².
• Notice the mass cancels. That is a useful check, and a common free-response question.

Example 2: energy

A ball is dropped from 5 m. How fast is it moving just before it hits the ground? Ignore air resistance.

• Energy is conserved: mgΔy = ½mv², so v = √(2gΔy) = √(2 × 9.8 × 5) = √98 ≈ 9.9 m/s.

Example 3: momentum in a collision

A 2 kg cart moving at 3 m/s hits a 1 kg cart at rest, and they stick together.

• Momentum before: 2 × 3 = 6 kg·m/s. After: 3v. So v = 2 m/s.
• Kinetic energy before: ½ × 2 × 9 = 9 J. After: ½ × 3 × 4 = 6 J. 3 J is converted to other forms, so the collision is inelastic.

Example 4: circular motion

A 1200 kg car rounds a flat bend of radius 50 m at 10 m/s. What force keeps it on the circle?

• F = ma_c = mv²/r = 1200 × 100/50 = 2400 N, toward the centre.
• On a flat road, static friction from the tyres provides this force.

Example 5: a spring oscillator

A 0.5 kg mass hangs on a spring with k = 200 N/m. Find its period.

• T = 2π√(m/k) = 2π√(0.0025) = 2π × 0.05 ≈ 0.31 s.
• The amplitude does not appear in the equation, so a bigger oscillation has the same period.

Example 6: buoyancy

A 0.002 m³ block is fully submerged in water (density 1000 kg/m³). Find the buoyant force.

• F_b = ρVg = 1000 × 0.002 × 9.8 = 19.6 N, whatever the block is made of.

Which equation, when?

• Asked for time? Kinematics or impulse, not energy.
• Asked for speed after a height or distance change? Energy is usually fastest.
• Two objects interacting briefly? Momentum.
• Something turning or balancing? Torque.
• Something repeating? Oscillation periods.

Practice questions

Try each one before opening the answer.