AP Physics 1 Exam Cram Review

Unit 1: Kinematics

• Vectors have magnitude and direction, while scalars have magnitude only.

• Distance is the length of the path taken between initial and final positions (scalar).

• Displacement is the straight-line distance between initial and final positions (vector).

• \Delta x=x_{f}-x_{i} , indicating the change in position along the x-axis.

• Distance an object travels is greater than or equal to the magnitude of its displacement.

• Average velocity equals displacement over change in time (vector).

• \vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}

• Average acceleration equals change in velocity over change in time (vector).

• \vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}

• Instantaneous velocity or acceleration is the value at a specific time.

• Uniformly Accelerated Motion (UAM) equations (kinematics equations) apply when acceleration is constant.

• There are 5 variables and 4 equations, knowing 3 variables allows solving for the other 2.

• Slope of a position vs. time graph is velocity.

• Slope of a velocity vs. time graph is acceleration.

• Area between the curve and the time axis on a velocity vs. time graph is change in position.

• Area between the curve and the horizontal time axis on an acceleration vs. time graph is change in velocity.

• Area above the horizontal axis is positive, below is negative.

• Vectors are broken into component vectors using sine and cosine trigonometric functions.

• The angle theta isn't always measured from the horizontal, so x-component doesn't always use cosine.

• Projectile motion occurs when the only force is gravity near the Earth's surface.

• Acceleration in the y-direction: \vec{a}_y = -9.81 \frac{m}{s^2} (Use -10 \frac{m}{s^2} on AP exams).

• UAM equations apply in the y-direction.

• Acceleration in the x-direction is zero, so constant velocity applies in the x-direction.

• Relative motion: Description of motion depends on the observer's frame of reference; often involves vector addition.

Unit 2: Force and Translational Dynamics

• Center of mass equation:

• Xcm=\frac{\sum\operatorname{mi}\cdot ri}{\sum mi}

• Can replace position with velocity or acceleration.

• Forces are vectors resulting from interactions between two objects.

• Free Body Diagrams (FBDs) show all forces acting on an object.

• Only force vectors are included in FBDs.

• Forces start at the center of mass (offset slightly if multiple forces act in the same direction).

• Never break forces into components in a free body diagram answer on an AP Physics exam.

• The force normal (caused by a surface) is perpendicular to the surface, pushing away.

• Tension in a rope is parallel to the rope, a pull.

• Newton’s First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with a constant velocity, unless acted upon by a net, external force.

• Inertia is the tendency to resist acceleration.

• Newton’s Second Law: \vec{a} = \frac{\sum \vec{F}}{m} , relates net force, mass, and acceleration.

• Translational equilibrium occurs when the net force on an object is zero, meaning the object is at rest or moving at a constant velocity.

• Newton’s Third Law: For every force object one exerts on object two, object two exerts a force on object one that is equal in magnitude and opposite in direction, and these forces act simultaneously.

• Gravitational force: F_g = mg , where g is the gravitational field strength.

• The direction of the force of gravity on an object is always towards the center of mass of the planet; down.

• Friction is parallel to the surface and opposes sliding motion, independent of the force applied.

• Kinetic friction: F_{fk}=\mu_{k}F_{n} , occurs when surfaces are sliding relative to one another.

• \mu_k (coefficient of kinetic friction) is dimensionless, non-negative, and experimentally determined.

• Static friction: F_{fs}=\mu_{s}F_{n} , occurs when surfaces are not sliding relative to one another.

• Static friction adjusts to prevent sliding.

• Friction does not depend on the contact surface area.

• Newton’s Law of Universal Gravitation: F_{g}=\frac{Gm1m2}{r^2} where G is the gravitational constant.

• Gravitational force is directed along a line connecting the centers of mass, directed towards the other mass.

• Local gravitational field (little g) is nearly constant on a planet's surface.

• Ideal spring force (Hooke’s Law): F_{spring} = -kx, where k is the spring constant and x is the displacement from equilibrium.

• The direction of the spring force is always toward equilibrium position.

• The negative sign indicates that the spring force and displacement are opposite in direction.

• The magnitude of the slope of a graph of spring force vs. displacement from equilibrium position is the spring constant k.

• Tangential velocity: Linear velocity of an object moving along a circular path, directed perpendicularly to the radius and parallel to the path.

• Centripetal acceleration: Acceleration directed inward toward the center of the circle.

• a_c = \frac{v^2}{r}

• Period (T): Time for one complete circle.

• Frequency (f): Revolutions per second.

• T = \frac{1}{f}

• Centripetal force: Net force in the in-direction causing centripetal acceleration, not a new force, never in a free body diagram.

Unit 3: Work, Energy, and Power

• Translational kinetic energy: KE = \frac{1}{2}mv^2

• Work: W = Fd \cos(\theta), amount of mechanical energy transferred into or out of a system.

• Work done by a conservative force is path-independent (e.g., gravity, spring force).

• Work done by a nonconservative force is path-dependent (e.g., friction, air resistance).

• Mechanical energy types: kinetic, gravitational potential, and elastic potential energy.

• Potential Energy: Energy stored in a system due to the positions of objects.

• Change in gravitational potential energy: \Delta U_g = mg \Delta h .

• General form for gravitational potential energy: U_{g}=-\frac{Gm1m2}{r^{}}

• Elastic potential energy: U_{s}=\frac{1}{2}kx^2

• Work and Energy are scalars.

• A system with only one object can only have kinetic energy.

• Energy changes are balanced by equivalent changes or energy transfer.

• Total mechanical energy remains constant if zero net work is done and zero work is done by nonconservative forces.

• When there is net work done on a system, energy is transferred between the system and its surroundings.

• Work done by friction equals the change in mechanical energy of the system.

• Work-energy principle: W_{net} = \Delta KE, always valid.

• When using energy equations, identify the system, initial point, final point, and horizontal zero line.

• Power: Rate at which energy changes with time.

• Average power: P_{avg} = \frac{W}{\Delta t}

• Instantaneous power: P = Fv \cos(\theta)

Unit 4: Linear Momentum

• Linear momentum (vector): \vec{p} = m\vec{v}

• During collisions and explosions, the net external force is negligibly small.

• Newton’s Second Law in terms of momentum: \vec{F}_{net} = \frac{\Delta \vec{p}}{\Delta t}

• Impulse (vector): \vec{J} = \Delta \vec{p} = \vec{F}_{avg} \Delta t

• Impulse equals the area under a force vs. time curve.

• \sum F=0\rightarrow J=0\rightarrow\Delta p=0\left(MOMENTUMREMAINSCONSTANT\right)

• If the net force on a system is zero, the velocity of the center of mass is constant.

• When the net force is nonzero, linear momentum is transferred between the system and the environment.

• Types of collisions:

  • Elastic: Kinetic energy is conserved.

  • Inelastic: Kinetic energy decreases.

  • Perfectly inelastic: Objects stick together.

• Most real-world collisions are inelastic.

• Linear momentum is conserved in all collisions.

Unit 5: Torque and Rotational Dynamics

• Angular displacement: \Delta\theta=\theta_{f}-\theta_{i}

• 1 \text{ revolution} = 360^\circ = 2\pi \text{ radians}

• Average angular velocity: \omega_{avg} = \frac{\Delta \theta}{\Delta t}

• Average angular acceleration: \alpha_{avg} = \frac{\Delta \omega}{\Delta t}

• Rigid objects maintain shape; all points have the same angular displacement, velocity, and acceleration.

• Uniformly Angularly Accelerated Motion (UAM) equations are analogous to UAM equations.

• Slope of angular position vs. time is angular velocity.

• Slope of angular velocity vs. time is angular acceleration.

• Area under angular acceleration vs. time is change in angular velocity.

• Area under angular velocity vs. time is change in angular position.

• Arc length: s = r\theta

• Tangential velocity: v_t = r \omega

• Tangential acceleration: a_t = r \alpha

• Radians are dimensionless, required for linear-rotational conversions.

• Centripetal acceleration: a_{c}=\frac{v^2}{r}=r\omega^2

• Accelerations in circular motion: angular, tangential, and centripetal.

• Angular acceleration is an angular quantity (\frac{rad}{s^2}).

• Tangential and centripetal accelerations are linear (\frac{m}{s^2}).

• Tangential acceleration is tangent to the circular path, perpendicular to the radius.

• Centripetal acceleration is perpendicular to the circular path, inward along the radius.

• Tangential and centripetal acceleration are always perpendicular to one another.

• Circular motion requires centripetal acceleration.

• Tangential acceleration changes the magnitude of tangential velocity.

• Centripetal acceleration changes the direction of tangential velocity.

• Angular displacement, velocity, and acceleration describe the entire rotating object, while arc length, tangential velocity, tangential acceleration, and centripetal acceleration describe a specific location.

• Torque: \tau = rF \sin(\theta), the ability of a force to cause angular acceleration.

• r_{\perp} is the lever arm.

• Use clockwise and counterclockwise to indicate torque direction in AP Physics 1.

• Force diagrams are used to show where forces act on rigid objects.

• Rotational inertia: I = mr^2 for a point particle, resistance to angular acceleration.

• Rotational inertia of a system is the sum of individual rotational inertias.

• Equations for rotational inertia of rigid objects with shape are provided on the exam.

• Parallel Axis Theorem: I = I_{CM} + md^2

• Rotational equilibrium means constant angular velocity.

• Newton’s First Law in Rotational Form: An object at rest remains at rest, and a rotating object maintains a constant angular velocity, unless acted upon by a net external torque or the distribution of the mass of the object changes.

• Newton’s Second Law in rotational form: \tau_{net} = I\alpha

• Static equilibrium: Both translational and rotational equilibrium; net torque about any axis is zero.

Unit 6: Energy and Momentum of Rotating Systems

• Translational Kinetic Energy: Objects whose center of mass is changing location have Translational Kinetic Energy.

• Rotational Kinetic Energy: KE_{rot} = \frac{1}{2}I\omega^2

• Total kinetic energy: KE{total} = KE{rot} + KE_{trans}

• Work done by a torque: W = \tau \Delta \theta

• Angular Momentum: L = I\omega

• Angular Momentum of a Point Particle: L = rmv sin(\theta)

• Rotational form of Newton’s Second Law: \tau_{net} = \frac{\Delta L}{\Delta t}

• Angular impulse: J_{ang} = \Delta L = \tau \Delta t

• Total angular momentum remains constant if the net torque is zero.

• Rolling without slipping: Equations for displacement, velocity, and acceleration of the center of mass are related to circular motion equations.

• v_{CM} = r\omega

• Rolling with slipping invalidates the rolling without slipping equations.

• Circular orbits: Total mechanical energy, gravitational potential energy, angular momentum, and kinetic energy are constant.

• Elliptical orbits: Total mechanical energy and angular momentum are constant, but gravitational potential and kinetic energy are not.

• Linear momentum does not remain constant. Angular momentum remains constant.

• Escape velocity: Initial speed needed to reach infinite distance with zero final velocity.

Unit 7: Oscillations

• Periodic motion repeats in equal time intervals.

• Simple Harmonic Motion (SHM) results from a restoring force proportional to displacement from equilibrium.

• Equilibrium position is where the net force is zero.

• Restoring force is always directed towards equilibrium.

• Period (T) is the time for one full cycle.

• Amplitude (A) is the maximum distance from equilibrium.

• Mass-spring system positions:

  • Position 1 (max displacement): displacement = A, velocity = 0, force and acceleration are max and directed left.

  • Position 2 (equilibrium): displacement = 0, velocity is max, force and acceleration = 0.

  • Position 3 (max negative displacement): displacement = -A, velocity = 0, force and acceleration are max and directed right.

• Period of a mass-spring system: T = 2\pi \sqrt{\frac{m}{k}}

• Restoring force is the spring force.

• Period of a simple pendulum: T = 2\pi \sqrt{\frac{L}{g}}(for \theta < 15^\circ).

• Restoring force is the component of gravity tangent to the motion.

• Frequency is the number of cycles per second.

• Position in SHM: x = A \cos(2\pi f t)

• Cosine and sine are phase-shifted by 90^\circ

• Total mechanical energy in SHM is constant: E = KE + PE

• Total energy of a mass-spring system: E = \frac{1}{2}kA^2 = \frac{1}{2}mv_{max}^2

Unit 8: Fluids

• Density: \rho = \frac{m}{V}

• Pressure: P = \frac{F}{A}

• Absolute pressure: P_{abs}=P_0+\varrho gh

• Gauge pressure: P_{gauge} = \rho g h, independent of container's cross-sectional area.

• Buoyant force: F_{B}=\varrho Vg

• Continuity equation:A_1v_1=A_2v_2

• Bernoulli’s equation: P_1+\frac12\varrho v_{1^{}}^2+\varrho gy_1=P_2+\frac12\varrho v_2^2+\varrho gy_2

• Bernoulli’s Principle: If fluid speed increases, fluid pressure decreases (assuming height is negligible).

• Torricelli’s Theorem: v = \sqrt{2gh}