AP Physics C Basic Terms and Formulas 🔧 😭

scalar

measurement based on quantity alone

example of scalar

speed

vector

measurement that has both/affected direction and magnitude

example of vectors

velocity

Magnitude/Length of Vectors l<a,b>l

√a²+b²

Addition of vectors a+b

(a₁a₂)+(b₁+b₂) = (a₁+b₁,a₂+b₂)

subtraction of vectors

(a₁a₂)-(b₁+b₂) = (a₁-b₁,a₂-b₂)

dot/scalar products of 2 vectors in 2D

measures how parallel the vectors are (scalar)

dot/scalar product formula

a∙b = a₁b₁+a₂b₂ = lal lbl cos Θ

cross product of 2 vectors a & b in 3D is a vector that …..

perpendicular to the plane containing a & b so the more it is perpendicular the bigger the cross product

if the vectors are parallel the cross product is ….

zero

displacement

the change of position over the given time interval (vector)

how to find displacement graphically

the area under the velocity-time

formula for displacement

r-r₀=∫₀^t vdt

velocity

the instantaneous rate of change of position with respect to time (vector)

how to find velocity graphically

the slope of the position-time graph

formula of velocity

dx/dt

average velocity

velocity over a time interval

how to find average velocity graphically

slope of a secant line on the position-time graph

formula of average velocity

∆r/∆t = 1/∆t ∫^t₀ adt

speed

the magnitude of velocity

formula of speed

lv(t)l

acceleration

the instantaneous rate of change (derivative) of velocity with respect to time and so equals the slope of the velocity-time graph

Total Distance

the total distance travel

total distance can be calculated….

as the integral of speed

total distance can be found graphically

the area under the graph of the absolute value of the velocity-time graph

shape of position-time graph if particle is a rest for a time

horiziontal

shape of position-time graph if particle is at rest for an instant

max or min or horizontal tangent

shape of position-time graph if the particle is turning around

max or min

shape of position-time graph if particle is moving to the right or up

positive increasing

shape of position-time graph if particle is moving to the left or down

positive decreasing

shape of position-time graph if particle is slowing down

magnitude of slope is decreasing

shape of position-time graph if particle is speeding up

magnitude of slope is increasing

shape of velocity-time graph if the particle is at rest for a time

constant at value 0

shape of velocity-time graph if particle is at rest for an instant

root

shape of velocity-time graph if the particle is turning around

changes from + to - or - to +

shape of velocity-time graph if the particle is moving to the right or up

positive

shape of velocity-time graph if the particle is moving to the left or down

negative

shape of velocity-time graph if the particle is slowing down

positive and decreasing or negative and increasing

shape of velocity-time graph if particle is speeding up

positive and increasing or negative and decreasing

for constant acceleration v_x=

v_x0+a_xt

for constant acceleration x=

x₀+v_x0t+1/2a_xt²

for constant acceleration v_x²=

v_x0²+2a_x(x-x₀)

center of mass

where all the mass is concentrated

where is the center of mass for an symmetric and uniform object

the geometric center

how to find a center of mass of an irregular shape

x_cm= ∑m_ixi / ∑m_i y_cm= ∑m_iy_i / ∑m_i

force

a push of a pull that can be administered at a distance or by contact

how is force measured

N=kg∙m/s²

forces administered at a distance

gravitational force (weight) and electric and magnetic

forces administered by contact

tension, normal force, contact force, applied force, drag (air resistance), friction, spring force

formula for gravitational force (weight)

W= mg

tension

a force counter acting gravity

normal force

the support force exerted by a surface upon an object in contact with it, acting perpendicular (normal) to that surface

contact force

any force that acts between two objects that are physically touching each other

applied force

any force applied to an object

drag (air resistance)

a resistive force acting opposite to the motion of an object moving through a fluid

friction

a contact force that resists the relative motion or attempted motion of two surfaces, solid layers, or materials sliding against each other

spring force

the restoring force exerted by a spring to return to its natural length when compressed or stretched

net force

the vector sum of all individual forces acting on an object, representing the overall effect of those forces, including magnitude and direction

formula for net force

F_net=ma

formula for friction

f=μN

formula for spring force

F_s=-k∆x where k=spring constant

what happens when k (the spring constant) is made larger

makes it tougher to change spring’s direction

Newton’s Third Law

if A exerts a force on B, then B exerts a force on A. These forces have the same magnitude and type of force just in opposite direction

internal forces

the agent and object of the force are both in the system

external forces

agent of the force is outside of the system

what kind of force can change motion of the system

external forces

Newton’s First Law

an object either remains at rest or moves at a constant speed without any extra forces (external)

What does the 1st law mean for net force

the net force = 0 because there is no acceleration → F_net=m(0)

Newton’s 2nd Lines

F_net=ma or F_net=m_totala_cm

If a force is parallel to it’s velocity it will…..

change the magnitude of velocity

If the force is perpendicular to velocity it will…..

change its direction

If a force is applied at an angle what needs to be considered

the components of the force