This AP Physics 1 equation sheet annotated guide organizes the most important formulas into a clear reference for problem solving and exam review. It helps students decide which equation fits a situation instead of memorizing formulas without context. The sheet is designed around the major AP Physics 1 themes: motion, forces, conservation laws, rotation, oscillations, waves, and circuits.
Annotations connect each formula to units, diagrams, and common use cases.
Key Facts
- For constant acceleration in one dimension, use , , and .
- Newton’s second law is , so acceleration points in the direction of the net force.
- Linear momentum is , and impulse changes momentum according to .
- Mechanical energy is conserved when only conservative forces do work, so .
- Work is , kinetic energy is , and gravitational potential energy near Earth is .
- For rotation, torque is , rotational inertia connects to angular acceleration through , and angular momentum is .
- For simple harmonic motion, the spring period is and the pendulum period for small angles is .
- For DC circuits, Ohm’s law is , electric power is , and series resistors add as .
Vocabulary
- Net force
- The vector sum of all forces acting on an object, written as .
- Impulse
- The change in momentum caused by a force acting over time, written as .
- Mechanical energy
- The total energy from motion and position, usually written as .
- Torque
- The rotational effect of a force, calculated by .
- Angular velocity
- The rate at which an object rotates, written as .
- Equivalent resistance
- A single resistance value that has the same effect as a group of resistors in a circuit, written as .
Common Mistakes to Avoid
- Using constant-acceleration equations when acceleration changes is wrong because equations like assume is constant.
- Treating force as the same as velocity is wrong because links force to acceleration, not directly to motion at constant speed.
- Ignoring vector directions in momentum problems is wrong because can be positive or negative depending on the chosen axis.
- Applying conservation of mechanical energy when friction does work is wrong because nonconservative work changes .
- Forgetting the lever arm in torque problems is wrong because only the perpendicular component creates torque, so .
Practice Questions
- 1 A cart starts from rest and accelerates at for . Find its final speed using .
- 2 A block is pushed with a net force of . Find its acceleration using .
- 3 A spring with is compressed by . Find the elastic potential energy using .
- 4 A student chooses momentum conservation for a collision problem instead of energy conservation. Explain what feature of the situation makes momentum conservation the safer starting point.
Understanding AP Physics 1 Equation Sheet Annotated
An equation becomes useful only after you define the system and choose directions. In motion problems, draw a line for the path and label one direction positive. Every velocity, displacement, and acceleration value must follow that choice.
A negative answer is often meaningful. It can show that an object moves opposite your chosen positive direction, not that the calculation failed. Constant acceleration equations apply only when acceleration stays the same during the time interval.
A position versus time graph shows velocity through its slope. A velocity versus time graph shows acceleration through its slope, while the area under it gives displacement. These graph links often reveal more than a formula alone.
For force problems, start with a free body diagram before writing any equations. Include only forces acting on the object you selected. Common forces include weight, normal force, tension, friction, and an applied push or pull.
Weight points downward near Earth. The normal force is perpendicular to a surface, so it does not always point upward. Friction opposes the relative slipping or the tendency to slip between surfaces.
Resolve angled forces into components that match your axes. Then apply the idea that net force equals mass times acceleration separately along each direction. A balanced force diagram means zero acceleration, though the object may still move at constant velocity.
Conservation methods depend on clear boundaries. Energy methods work well when a problem compares two positions, such as a skateboard rolling down a ramp or a cart compressing a spring. If friction, air resistance, or an outside push matters, mechanical energy changes.
You may need to include work done by those forces. Momentum is especially useful for short interactions such as a bat striking a ball or two carts colliding. During the collision, external impulse must be negligible for total momentum to remain constant.
Momentum has direction, so treat it with positive and negative signs along one chosen axis. Impulse explains why airbags, helmets, and crash cushions reduce force by increasing the stopping time.
Rotation uses familiar ideas with different quantities. A force creates the greatest turning effect when it acts far from the pivot and perpendicular to the lever arm. This explains why door handles sit far from hinges and why pushing sideways on a wrench works best.
Rotational inertia depends on how mass is spread out, not just on total mass. Mass farther from the axis makes an object harder to speed up or slow down in rotation. In waves, separate the motion of the medium from the motion of the disturbance.
Frequency tells how many cycles occur each second, while wavelength measures the distance between matching points. In circuits, trace complete paths and identify which elements share the same current or the same voltage. Check units at every stage.
A final answer in meters, seconds, joules, or watts should match the physical quantity you were asked to find. Unit checks catch many mistakes before they reach the final line.