AP Physics C: Mechanics Full Review

acceleration due to gravity, g

acceleration due to gravity, g

acceleration of an object as a result of gravity

average acceleration

the rate of change of velocity; the change in velocity over time

average speed, v

the total distance traveled divided by elapsed time

average velocity, v

the displacement divided by the time over which displacement occurs under constant acceleration

displacement, Δx

the change in position of an object

distance traveled

the total length of the path traveled between two positions

elapsed time, Δt

the difference between the ending time and the beginning time

free fall

the state of movement that results from gravitational force only

instantaneous acceleration, a

acceleration at a specific point in time

instantaneous speed, v

the absolute value of the instantaneous velocity

instantaneous velocity, v

the velocity at a specific instant or time point

kinematics

the description of motion through properties such as position, time, velocity, and acceleration

position, x

the location of an object at a particular time

total displacement, Δx

the sum of individual displacements over a given time period

two-body pursuit problem

a kinematics problem in which the unknowns are calculated by solving the kinematic equations simultaneously for two moving objects

acceleration vector, a

instantaneous acceleration found by taking the derivative of the velocity function with respect to time in unit vector notation

angular frequency, ω

rate of change of an angle with which an object that is moving on a circular path

centripetal acceleration

component of acceleration of an object moving in a circle that is directed radially inward toward the center of the circle

displacement vector, Δr

vector from the initial position to a final position on a trajectory of a particle

position vector, r

vector from the origin of a chosen coordinate system to the position of a particle in two- or three-dimensional space

projectile motion

motion of an object subject only to the acceleration of gravity

range

maximum horizontal distance a projectile travels

reference frame

coordinate system in which the position, velocity, and acceleration of an object at rest or moving is measured

relative velocity

velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame

tangential acceleration

magnitude of which is the time rate of change of speed. Its direction is tangent to the circle.

time of flight

elapsed time a projectile is in the air

total acceleration

vector sum of centripetal and tangential accelerations

trajectory

path of a projectile through the air

velocity vector, v

vector that gives the instantaneous speed and direction of a particle; tangent to the trajectory

dynamics

study of how forces affect the motion of objects and systems

external force

force acting on an object or system that originates outside of the object or system

force, F

push or pull on an object with a specific magnitude and direction; can be represented by vectors or expressed as a multiple of a standard force

free fall

situation in which the only force acting on an object is gravity

free-body diagram

sketch showing all external forces acting on an object or system; the system is represented by a single isolated point, and the forces are represented by vectors extending outward from that point

Hooke's law

in a spring, a restoring force proportional to and in the opposite direction of the imposed displacement

inertia

ability of an object to resist changes in its motion

inertial reference frame

reference frame moving at constant velocity relative to an inertial frame is also inertial; a reference frame accelerating relative to an inertial frame is not inertial

law of inertia

see Newton's first law of motion

net external force

vector sum of all external forces acting on an object or system; causes a mass to accelerate

newton

SI unit of force; 1 N is the force needed to accelerate an object with a mass of 1 kg at a rate of 1 m/s2

Newton's first law of motion

body maintains constant velocity in an inertial reference frame unless acted on by a net external force; also known as the law of inertia

Newton's second law of motion

acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system and is inversely proportional to its mass

Newton's third law of motion

whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts

normal force

force supporting the weight of an object, or a load, that is perpendicular to the surface of contact between the load and its support; the surface applies this force to an object to support the weight of the object

tension

pulling force that acts along a stretched flexible connector, such as a rope or cable

thrust

reaction force that pushes a body forward in response to a backward force

weight

force due to gravity acting on an object of mass

balanced

Equilibrium is achieved when the forces on a system are ___________.

external

An ___________ force acts on a system from outside the system, as opposed to internal forces, which act between components within the system.

mass, m

the quantity of matter in a substance

systems

Two equal and opposite forces do not cancel because they act on different ___________ .

noninertial

Real forces have a physical origin, whereas fictitious forces occur because the observer is in an accelerating or ___________ frame of reference.

banked curve

curve in a road that is sloping in a manner that helps a vehicle negotiate the curve

centripetal force

any net force causing uniform circular motion

Coriolis force

inertial force causing the apparent deflection of moving objects when viewed in a rotating frame of reference

drag force

force that always opposes the motion of an object in a fluid; unlike simple friction, it is proportional to some function of the velocity of the object in that fluid

friction

force that opposes relative motion or attempts at motion between systems in contact

ideal banking

sloping of a curve in a road, where the angle of the slope allows the vehicle to negotiate the curve at a certain speed without the aid of friction between the tires and the road; the net external force on the vehicle equals the horizontal centripetal force in the absence of friction

inertial force

force that has no physical origin

kinetic friction

force that opposes the motion of two systems that are in contact and moving relative to each other

noninertial frame of reference

accelerated frame of reference

static friction

force that opposes the motion of two systems that are in contact and are not moving relative to each other

terminal velocity

constant velocity achieved by a falling object, which occurs when the weight of the object is balanced by the upward drag force

coefficient of friction, µ

A proportionality constant empirically determined relating the frictional force to the normal force.

average power, P

work done in a time interval divided by the time interval

kinetic energy, K

energy of motion, one-half an object's mass times the square of its speed

net work, W

work done by all the forces acting on an object

power, P

rate of doing work with respect to time

work, W

done when a force acts on something that undergoes a displacement from one position to another

work done by a force

integral, from the initial position to the final position, of the dot product of the force and the infinitesimal displacement along the path over which the force acts

work-energy theorem

net work done on a particle is equal to the change in its kinetic energy

negative

The work done against a force is the __________ of the work done by the force.

particles

The kinetic energy of a system is the sum of the kinetic energies of all the __________ in the system.

relative, positive, motion

Kinetic energy is __________ to a frame of reference, is always __________, and is sometimes given special names for different types of __________.

work-energy

Because the net force on a particle is equal to its mass times the derivative of its velocity, the integral for the net work done on the particle is equal to the change in the particle's kinetic energy. This is the __________ theorem

conservative force

force that does work independent of path

conserved quantity

one that cannot be created or destroyed, but may be transformed between different forms of itself

energy conservation

total energy of an isolated system is constant

equilibrium point

position where the assumed conservative, net force on a particle, given by the slope of its potential energy curve, is zero

exact differential

is the total differential of a function and requires the use of partial derivatives if the function involves more than one dimension

mechanical energy, E

sum of the kinetic and potential energies

non-conservative force

force that does work that depends on path

potential energy, U

function of position, energy possessed by an object relative to the system considered

potential energy diagram

graph of a particle's potential energy as a function of position

potential energy difference, ΔU

negative of the work done acting between two points in space

turning point

position where the velocity of a particle, in one-dimensional motion, changes sign

zero

Since only differences of potential energy are physically meaningful, the __________ of the potential energy function can be chosen at a convenient location

independent, zero

A conservative force is one for which the work done is __________ of path. Equivalently, a force is conservative if the work done over any closed path is __________

depends

A non-conservative force is one for which the work done __________ on the path.

center of mass

weighted average position of the mass

closed system

system for which the mass is constant and the net external force on the system is zero

elastic

collision that conserves kinetic energy

explosion

single object breaks up into multiple objects; kinetic energy is not conserved in explosions

external force

force applied to an extended object that changes the momentum of the extended object as a whole

impulse, J

effect of applying a force on a system for a time interval; this time interval is usually small, but does not have to be

impulse-momentum theorem

change of momentum of a system is equal to the impulse applied to the system

inelastic

collision that does not conserve kinetic energy

internal force

force that the simple particles that make up an extended object exert on each other. Internal forces can be attractive or repulsive

Law of Conservation of Momentum

total momentum of a closed system cannot change

linear mass density, λ

expressed as the number of kilograms of material per meter