Physics & Math -- Kinematics and Dynamics

Length

meter (m)

Mass (not weight)

kilogram (kg)

Time

second (a)

Current

ampere (coulomb/second) (A)

Amount of substance

mole (mol)

Temperature

kelvin (K)

Luminous intensity

candela (cd)

Vectors

quantities that have both a magnitude and a direction

Scalars

quantities without direction

Vector addition may be accomplished using

tip-to-tail method or breaking a vector into its components and using the Pythagorean theorem

Vector subtraction is accomplished by

changing the direction of the second vector, and then using the tip-to-tail method or breaking the vector into its components and using the Pythagorean theorem

Multiplying a vector by a scalar

changes the vector's magnitude

If multiplying a vector by a negative scalar

changes vector's magnitude and direction

multiplying two vectors using dot product

results in scalar quantity

Dot product

A*B = ABcosx

Cross product

A*B = ABsinx

Dot product definition

product of the vectors' magnitudes and the cosine of the angle between the vectors

Multiplying two vectors using cross product

results in vector quantity

Cross product definition

the product of the vectors' magnitudes and the sine of the angle between the vectors

What is used to determine the resultant vector's direction?

right hand rule

Displacement

the vector respresentation of a change in position

Displacement is

path independent and equivalent to the straight-line distance between the start and end location

Distance

scalar quantity that records the total length of path traveled

Velocity

the speed of an object in a particular direction

Average velocity

the total displacement divided by the time interval during which the displacement occurred

Average speed

total distance divided by total time

instantaneous velocity

the limit of the change in displacement over time as the change in time approaches zero

Instantaneous speed

magnitude of instantaneous velocity vector

Acceleration

vector representation of the change in velocity over time

Force

any push or pull that has the potential to result in an acceleration

Gravity

Attractive force between two objects that depends on the masses of the objects and the distance between them

Force of gravity equation

Fg = (G m1 m2) / r^2

Friction

A force that opposes motion between two surfaces that are in contact

Static friction

Friction that acts on objects that are not in motion relative to each other

Kinetic friction

friction between two objects that are in motion relative to each other

Coefficient of friction

Depends on the two materials in contact

The coefficient of static friction is always _______ than the coefficient of kinetic friction.

higher

Kinetic friction equation

fk = uk N

Static friction equation

fs = us N

Force of gravity (weight) of an object

Fg = mg

Mass

a measure of the inertia of an object (its amount of material)

Weight

the force experienced by a given mass due to its gravitational attraction to earth

Parallel component of gravitational force on an object

Fg,|| = mg sinx

Perpendicular component of gravitational force on an object

Fg,⟂ = mg cosx

Newton's First Law (Law of Inertia)

An object in motion (or at rest) will tend to stay in motion (or at rest) until it is acted upon by an outside force.

Newton's second law

any acceleration is the result of the sum of the forces acting on the object and its mass

Newton's third law

any two objects interacting with one another experience equal and opposite forces as a result of their interaction

Newton's first law equation

F = ma = 0

Newton's second law equation

F=ma

Newton's third law equation

Fab = -Fba

Linear motion

Movement in a straight line

Linear motion includes

free fall and motion in which the velocity and acceleration vectors are parallel or antiparallel

Projectile motion

contains both an x- and y-component. Assuming negligible air resistance, the only force acting on the object is gravity

Inclined planes

a sloping surface that reduces the amount of force required to do work; consider the dimensions of being parallel and perpendicular to the surface

Velocity equation solving for v

v = v0 + at

Velocity equation solving for x

x = v0t + at^2/2

Velocity equation solving for v^2

v^2 = v0^2 + 2ax

Constant velocity equation solving for x

x = vt

Circular motion

is any motion in which an object is moving along a curved path; best thought of as having both radial and tangential dimensions

Uniform circular motion

the movement of an object at a constant speed around a circle with a fixed radius

In uniform circular motion, the only force is

centripetal force

In uniform circular motion, centripetal force points _________________ and the instantaneous velocity vector always points ___________.

radially inward; tangentially

Centripetal force equation

Fc = mv^2/r

Torque equation

τ = r x F = rFsinx

Free body diagrams

a diagram showing all the forces acting on an object

Free body diaframs are useful for

equilibrium and dynamics problems

Translational equilibrium

State where the sum of the forces acting on an object is zero, giving it no net acceleration.

An object in translational equilibrium

has a constant velocity and may or may not be in rotational equilibrium

Rotational equilibrium

State where the sum of the torques acting on a body is zero, giving it no net angular acceleration.

Rotational motion may consider any _____, but the center of mass is most commonly used

pivot points

An object in rotational equilibrium

has constant angular velocity

On the MCAT, the angular velocity is

usually zero