AP Physics 1 Formula Sheet Cheat Sheet

This AP Physics 1 formula sheet covers the major equation groups students use in algebra-based mechanics, rotation, waves, and basic circuits. It helps students quickly choose relationships during homework, labs, and exam review. A clear reference is useful because many AP problems require connecting several models rather than memorizing one equation.

Key Facts

For constant acceleration in one dimension, use $v = v_0 + at$ , $x = x_0 + v_0t + \frac{1}{2}at^2$ , and $v^2 = v_0^2 + 2a\Delta x$ .
Newton's second law is $\sum F = ma$ , and the net force must be found from all forces acting on the object.
Common force models include weight $F_g = mg$ , kinetic friction $F_k = \mu_k F_N$ , static friction $F_s \le \mu_s F_N$ , and spring force $F_s = -kx$ .
Work and energy are related by $W_{net} = \Delta K$ , where $K = \frac{1}{2}mv^2$ , $U_g = mgh$ , and $U_s = \frac{1}{2}kx^2$ .
Linear momentum is $p = mv$ , impulse is $J = F\Delta t = \Delta p$ , and total momentum is conserved when the net external force is zero.
Rotational motion uses $\tau = rF\sin\theta$ , $\sum \tau = I\alpha$ , $K_{rot} = \frac{1}{2}I\omega^2$ , and $L = I\omega$ .
Circular and gravitational motion use $a_c = \frac{v^2}{r}$ , $F_g = G\frac{m_1m_2}{r^2}$ , and $U_g = -G\frac{m_1m_2}{r}$ .
Waves and circuits use $v = f\lambda$ , $T = \frac{1}{f}$ , $V = IR$ , $P = IV$ , and $P = I^2R = \frac{V^2}{R}$ .

Vocabulary

Net force: Net force is the vector sum of all forces on an object, and it determines acceleration through $\sum F = ma$ .
Work: Work is energy transferred by a force over a displacement, calculated by $W = Fd\cos\theta$ .
Momentum: Momentum is the product of mass and velocity, given by $p = mv$ .
Torque: Torque is the rotational effect of a force, calculated by $\tau = rF\sin\theta$ .
Angular velocity: Angular velocity is the rate of change of angular position, represented by $\omega = \frac{\Delta \theta}{\Delta t}$ .
Ohm's law: Ohm's law relates voltage, current, and resistance using $V = IR$ .

Common Mistakes to Avoid

Using constant-acceleration equations when acceleration is not constant is wrong because equations like $v = v_0 + at$ assume one fixed value of $a$ .
Treating forces as scalars is wrong because $\sum F = ma$ must be applied separately in each direction with correct signs.
Forgetting that static friction is an inequality is wrong because $F_s \le \mu_s F_N$ means static friction adjusts up to a maximum value.
Mixing mass and weight is wrong because mass is $m$ in kilograms while weight is a force given by $F_g = mg$ in newtons.
Using energy conservation when nonconservative work is present is wrong unless the equation includes $W_{nc} = \Delta K + \Delta U$ .

Practice Questions

1 A cart starts from rest and accelerates at $2.5\,\text{m/s}^2$ for $4.0\,\text{s}$ . Find its final speed and displacement.
2 A $6.0\,\text{kg}$ block is pulled with a horizontal force of $40\,\text{N}$ across a surface where $\mu_k = 0.20$ . Find the acceleration.
3 A spring with $k = 300\,\text{N/m}$ is compressed $0.10\,\text{m}$ . Find the elastic potential energy stored in the spring.
4 A student says momentum is always conserved in every collision. Explain when this statement is valid and why external forces matter.

Understanding AP Physics 1 Formula Sheet

A formula becomes useful only after the physical situation has been modeled. Start by choosing the object or group of objects you will study. Then identify the time interval or position change that matters.

Constant acceleration equations only fit motion when acceleration stays unchanged. A ball rising under gravity can often fit this model if air resistance is ignored. A car in traffic usually cannot.

Define a positive direction before using any motion equation. Velocity, acceleration, displacement, force, and momentum can then be positive or negative. Many wrong answers come from mixing up a distance, which has no direction, with a displacement, which does.

Force problems become clearer when you draw a free body diagram. Show only forces acting on the chosen object. Do not draw forces the object exerts on something else.

On an incline, weight points straight down, while the normal force points perpendicular to the surface. Friction points opposite the actual motion or the tendency to slide. The normal force is not always equal to weight.

It changes when an object is pushed at an angle, moves on a slope, or rides in an elevator. Add force components separately in each direction.

A zero net force means no acceleration, not necessarily no motion. An object can move at a steady speed while the forces balance.

Energy methods are useful when forces act over a distance, especially when the path is complicated. They can avoid finding the time of motion. First decide which objects belong in the system.

If a falling object and Earth are in one system, gravitational potential energy belongs inside the system. If friction acts, some organized mechanical energy becomes thermal energy. Momentum methods work best during short interactions such as collisions, recoil, and explosions.

The key idea is that internal forces can change each object’s momentum, yet they cannot change the total momentum of an isolated system. External impulses matter when a force from outside acts for a measurable time. In every collision problem, state clearly whether objects stick together, bounce apart, or move separately afterward.

Rotation uses many familiar ideas, but distance from the axis matters. The same force produces a larger turning effect when applied farther from the pivot and more nearly perpendicular to the lever arm. Mass spread far from an axis makes an object harder to speed up rotationally.

This explains why a door opens more easily at its handle than near its hinges. For rolling without slipping, translation and rotation are linked, so a rolling object has two forms of kinetic energy. In waves, track what travels through the material and what merely oscillates in place.

In circuits, follow charge through each possible path and use units as a check. Voltage is energy transferred per unit charge, current is charge flow per unit time, and resistance describes opposition to that flow. Unit checks often reveal an incorrect equation choice before any calculation is finished.

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AP Physics 1 Formula Sheet Cheat Sheet

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Understanding AP Physics 1 Formula Sheet