MCAT Physics and Math Review 2024-2025

What are included as SI units?

meter (m), kilogram (kg), second (s), ampere (A), mole (mol), kelvin (K), and candela (cd)

Vectors

physical quantities that have both magnitude and direction

What quantities are considered vector?

displacement, velocity, acceleration, and force

Scalars

quantities without direction

What are some scalar quantities?

magnitude of vectors, speed, coefficients of friction

What is a method to achieve vector addition?

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

What is a method to achieve vector subtraction?

changing the direction of the subtracted vector and the following the procedures for vector addition

What changes when multiplying a vector by a scalar quantity?

the magnitude changes and direction may reverse

What is the product of two multiplied vectors using dot product?

a scalar quantity representing the product of the vectors' magnitudes and the cosine of the angle between them

What is the product of two multiplied vectors using cross product?

a vector quantity representing the product of vectors' magnitudes and the sine angle between them; right hand rule is used to determine the resultant vector's direction

Displacement

the vector quantity representing the change in position

What is displacement equivalent to?

the straight-line distance between the start and end locations

Distance

scalar quantity that reflects the path traveled

Velocity

the vector representing the change in displacement with respect to time

Average velocity

delta-x / delta-t

Average speed

the total distance traveled divided by the total time

Instantaneous velocity

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

Instantaneous speed

the magnitude of the instantaneous velocity vector

Force

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

Gravity

the attractive force between two objects as a result of their masses

Friction

a force that opposes motion as a function of electrostatic interactions at the surfaces of two objects

Where does static friction exist?

between two objects that aren't in motion relative to each other

Where does kinetic friction exist?

between two objects that are in motion relative to each other

Is kinetic friction constant?

yes

What does coefficient of friction depend on?

the two materials in contact

What is teh relationship between the coefficient of static friction and teh coefficient of kinetic fiction?

the coefficient of static friction is always higher than the coefficient of kinetic friction

Are mass and weight synonymous?

No

Mass

the measure of the inertia of an object

Weight

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

Acceleration

the vector representing the change in velocity over time

Newton's first law (law of inertia)

an object will remain in at rest or move with a constant velocity if there is no net force on the object

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

Linear motion

velocity and acceleration vectors are parallel or antiparallel

What is included in linear motion?

free fall

What does projectile motion include?

an x- and y- component

If air resistance is negligible, what is the only force acting on an object in projectile motion?

gravity

What are inclined planes an example of?

two-dimensional movement

What is the only force in uniform circular motion?

centripetal force that points radially inward

Free body diagrams

representation of the forces that are acting on an object

Translational equilibrium

object has constant velocity, and may or may not also be in rotational equilibrium; occurs in the absence of any net forces acting on an object

Rotational equilibrium

object has constant angular velocity; occurs in the absence of any net torques acting on an object

Energy

property of a system that enables it to do something or make something happen, including the capacity to do work

What are the SI units for energy?

joules (J)

Kinetic energy

energy associated with the movement of objects

What does kinetic energy depend on?

mass and speed squared

Potential energy

energy stored within a system

What are the forms of potential energy?

gravitational, elastic, electrical, and chemical

Gravitational potential energy

related to the mass of an object and its height above a zero-point (datum)

Elastic potential energy

related to the spring constant and the degree of stretch or compression of a spring squared

Spring constant

a measure of the stiffness of a spring

Electrical potential energy

exists between two charged particles

Chemical potential energy

the energy stored in the bonds of compounds

Total mechanical energy

the sum of its kinetic and potential energies

Conservative forces

path independent forces that do not dissipate the mechanical energy of the system

When is the total mechanical energy of a system conserved?

when only conservative forces are acting on an object

What are some examples of conservative forces?

gravity and electrostatic forces; elastic forces are nearly conserved

Nonconservative forces

forces that are path dependent and cause dissipation of mechanical energy from a system

Where is mechanical energy lost to?

thermal or chemical energy

What are some examples of nonconservative forces?

friction, air resistance, and viscous drag

Work

process by which energy is transferred from one system to another

What are some ways that work can be expressed?

as the dot product of force and displacement or the product of force and distance traveled with teh cosine of the angle between the two

What is another way work can be expressed?

the area under a pressure-volume (P-V) curve

Power

the rate at which work is done or energy is transferred

What are teh SI units for power?

watt (W)

Work-energy theorem

when net work is done on or by a system, the system's kinetic energy will change by the same amount; the work done on or by a system can be transferred to other forms of energy as well

Mechanical advantage

the factor by which a simple machine multiplies the input force to accomplish work

What are the six simple machines?

inclined plane, wedge, wheel and axle, lever, pulley, and screw

Simple machines

provide benefit of mechanical advantage

What does mechanical advantage do?

make it easier to accomplish a given amount of work because the input force necessary to accomplish the work is reduced; the distance through which the reduced input force must be applied, however, is increased by the same factor

Load

the output force of a simple machine, which acts over a given load distance to determine the work output of the simple machine

Effort

the input force of a simple machine, which acts over a given effort distance to determine the work input of the simple machine

Efficiency

the ration of the machine's work output to work input when nonconservative forces are taken into account

How do you calculate the x-component of a vector?

X = Vcos(theta)

How do you calculate the y-component of a vector?

Y = Vsin(theta)

Pythagorean theorem

X^2 + Y^2 = V^2; V = SQRT(X^2 + Y^2)

Determination of direction from component vectors

theta = tan^-1(Y/X)

Dot product

A . B = |A| |B| cos(theta)

Cross product

A x B = |A| |B| sin(theta)

Universal gravitation equation

Fg = (Gm1 * m2)/r^2

Static friction

0 < fs < μsN

Kinetic friction

fk = μkN

Force of gravity (weight on earth)

Fg = ma

Average acceleration

delta-v / delta-t

Instantaneous acceleration

a = lim (as change in time approaches 0) delta-v/delta-t

Newton's first law equation

Fnet = ma = 0

Newton's second law equation

Fnet = ma

Newton's third law equation

FAB = -FAB

Kinematics (no displacement)

v = v0 + at

Kinematics (no final velocity)

x = v0t + (at^2)/2

Kinematics (no time)

v^2 = v0^2 + 2ax

Kinematics (no acceleration)

x = vt

Component of gravity on an inclined plane

Fg.|| = mg sin(theta); Fg| = mg cos(theta)

Centripetal force equation

Fc = (mv^2)/r

Torque equation

T = r x F = rFsin(theta)

Kinetic energy equation

K = (1/2)mv^2

Gravitational potential energy equation

U = mgh

Elastic potential energy equation

U = (1/2)kx^2

Total mechanical energy equation

E = U + K

Conservation of mechanical energy equation

delta-E = delta-U + delta-K = 0