**instantaneous velocity (v _{o})**.

**Instantaneous velocity** is the direction and magnitude of the rate of change for distance per unit time.

**v _{o} = **

**Δ**

**x / t**

or: **v _{o} = p/m**

Where p is the object's momentum and m is its mass.

**average velocity (v _{ave})**

**Average velocity** is the total distance and direction traveled from an initial position, divided by the total time.

**v _{ave} = Δx_{total} / Δt_{total}**

or: **v _{ave} = (v_{f} + v_{i})/2**

Note: the second equation assumes constant acceleration, which is also assumed on the AP exam unless specified otherwise.

**acceleration**

**Acceleration **is the rate at which velocity changes per unit of time.

**a = Δv / ****t**

or: **a = Δx / t ^{2}**

What is the acceleration always associated with an object in free fall?

9.8 m/s^{2}

This is the acceleration due to gravity, commonly called g. On the AP exam, any falling object is assumed to be in free fall (no air resistance) unless told otherwise.

Note: while it's convenient to use 10 m/s^{2} for calculations, the AP exam expects you to still choose the correct answer mathematically.

Describe Newton's first law of motion.

aka the **Law of Inertia:** An object in motion will continue with constant velocity unless acted on by a net force.

Similarly, an object at rest will continue to remain at rest until acted on by a net force.

What must be true about the acceleration of an object, if all forces acting on it cancel?

The object has zero acceleration.

Since all forces cancel to be zero, there is not a net force and there will not be a change in velocity. If there is no change in velocity, that is the same as no acceleration.

What is the relationship between force, mass, and acceleration in Newton's second law of motion?

**F _{net} = ma**

Note: net force and acceleration are both vectors, and must be pointing in the same direction.

What is the proportional change in force to make an object move with twice its original acceleration?

Twice the original force must be applied.

From Newton's second law, F=ma. Force and acceleration are directly proportional.

How does Newton's third law of motion describe the forces between two objects?

**F _{1on2} = -F_{2on1}**

For every force from one object on a second, there is an equal and opposite force from the second back on the first.

What magnitude of force must exist from apple to an orange in free space, if it's found that there is a force from the orange to the apple of 5N.

5N

From Newton's third law, every force excerted must have an equal and opposite force. The negative sign is already factored in, since the question specified direction.

**Weight**

**Weight **is explicitly the force on an object due to gravity. **W=mg**

Weight if often confused with mass; an object with one weight on Earth will have a different, lesser, weight on the moon, but its mass will remain constant.

**mechanical advantage**

**Mechanical advantage** is the multiplication of a force using a mechanical device. A small force exerted over a large distance is transformed into a larger force over a smaller distance.

On the AP exam, mechanical advantage appears primarily in problems including levers.

the **kinetic energy** of an object

An object's **kinetic energy** is the energy resulting from its motion.

Kinetic energy is defined as:

**KE = ½mv ^{2}**

where m is the object's mass and v is its speed. The units of kinetic energy are Joules, just like all other forms of energy.

**fulcrum **and **lever arm**

The **fulcrum **is the point of an object that remains fixed during rotation.

The **lever arm** is the distance from the fulcrum where a force is applied, to create rotation around the fulcrum.

**torque**

**Torque **is the ability of a force to create a change in the angular orientation of an object, by rotation about a fulcrum point. Torque can also be thought of as the component of work perpendicular to a lever arm.

The SI unit of torque is the **N-m**.

Briefly describe the **Bohr Theory **of the atom.

The** Bohr Theory** states:

- Electrons can only exist in fixed orbits or energy levels.
- These energy levels are at specific distances from the nucleus.
- Any energy emitted/absorbed from/by an atom will be the result of an electron jumping from one energy level to another.

the **atomic number, Z,** of an element

The **atomic number **of an element is the number of protons contained within the element's nucleus.

Atomic number is a characteristic property of an element. For instance, all atoms with 1 proton in their nucleus are hydrogen atoms, regardless of how many neutrons exist in the nucleus.

**buoyancy**

**Buoyancy** is the tendency of an object to weigh less when partially or fully submerged in a liquid.

Buoyancy is caused by the liquid displaced by the object. The liquid pushes up on the object with a force equal to the weight of the liquid displaced.

**surface tension** of a fluid

**Surface tension** is the ability of a fluid's surface to resist an external force.

Surface tension is caused by attractive forces between the molecules of the fluid. It is responsible for the spherical shape of soap bubbles and the ability to skip a stone off the surface of a lake.

What is the formula for converting between temperature in Centigrade and Fahrenheit?

T_{F} = (9/5)*T_{C} + 32

T_{F} = Fahrenheit Temperature

T_{C} = Celsius Temperature

Some standard conversions to memorize:

- 32º F = 0º C
- 77º F = 25º C
- 212º F = 100º C

a **conductor**

A **conductor **contains many electrical charges within the medium, and they are relatively moveable.

Common conductors are usually metals with high atomic weight, such as silver, copper, and gold.

an **insulator**

An **insulator **has few free electrical charges within the medium, and those are difficult to move.

Common insulators are as glass, quartz, rubber and teflon.

a **battery**

An **electrical battery** (or electrochemical cell) is a device that produces a flow of electrons from anode to cathode.

The necessary electrical energy is created by undergoing redox chemical reactions in the cell.

**voltage**

**Voltage (electric potential)** is the electrical energy per unit charge necessary to move a test charge against the electric field of a fixed charge.

**resistance**

**Resistance **is a measure of how difficult it is to pass current through some object. Many factors affect resistance, including: cross-sectional area, length, and general resistivity.

Though all materials have some resistance at room temperature, super-cooled superconductors have a resistance of zero.

What must have happened to the voltage supplied to a fixed resistance circuit, if the current suddenly drops to half original?

The voltage must have also dropped to half.

From Ohm's law: V=*I*R

Since R is held constant, V and *I* are directly proportional. Halving voltage means current must be halved also.

What must have happened to the resistance in a fixed voltage circuit, if the current suddenly doubles?

The resistance must have dropped to 1/2 original.

From Ohm's law: V=*I*R

Since V is held constant, R and *I* are inversely proportional. Doubling current means resistance must be halved.

What does this symbol stand for in a circuit diagram?

This is a battery. Batteries will always have a larger positive terminal (labeled +) and a smaller negative terminal (labeled –).

Conventional current always flows from + to – around the circuit.

What does this symbol stand for in a circuit diagram?

This is a resistor. Resistors impede current flow and have units of ohms.

What does this symbol stand for in a circuit diagram?

This is a capacitor. Capacitors store charge and have units of farads.