Physics Equations

One dimensional : velocity

V = V₀+at

One dimensional: Position

x = x₀ + v₀t + ½ at²

Newtons second law

∑F=ma (vecotor)

Force of kinetic Friction

F_k=𝜇_kN (direction of friction is opposite of motion)

Force of Static Friction

F_s=𝜇_sN (direction of friction opposite motion)

F_s,max=𝜇_sN (direction opposite of motion)

Centripetal force

a_cp=v²/r

direction is towards center or circle

F_cp=m(v²/r)

direction is towards the center of the circle

Projectile motion horizontal components equatiosn for velocity and position based on a=?

a= 0 (only gravity is working and thats vertical)

v=v_0,x

x=x₀+v_0,xt

Projectile motion vertical components equatiosn for velocity and position based on a=?

a = -g (acceleration due to gravity)
v = v_0,y - gt
y = y₀ + v_0,yt - ½ gt²

Newtons second law vector decomposition for horizontal components

∑F_x = ma_x

F_g,x + F_n,x + F_k,x = ma_x

Newtons second law vector decomposition for vertical components

∑F_y = ma_y

F_g,y+ F_n,y + F_k,y = ma_y

Centripetal acceleration

∑F_radial = ma_cp = mv²/r

Kinetic energy (linear/translational only)

K=1/2mv²

Linear momentum, which is a vector equation

p(vector)=mv(vector)

Rotational Kinematic equation: velocity

w=w_o+𝛼𝑡

Rotational Kinematic equation: position

𝜃 = 𝜃₀ + 𝜔₀𝑡 + 1/2 𝛼𝑡²

Rotational Kinetic Energy

K=1/2 Iw²

Linear/Translational and rotational kinetic energy

K=1/2mv²+1/2Iw²

Definition of torque

𝜏 = 𝑟 𝐹 sin 𝜃
where 𝜃 is the angle between the r and F vectors

Newtons Second Law for rotational motion - this equation is not a vector

Σ𝜏 = 𝐼𝛼

Angular Momentum

𝐿 = 𝑟 𝑝 sin 𝜃
where 𝜃 is the angle between the r and p vectors

time

t —> t

position

x —> 𝜃

velocity

v —> 𝜔

acceleration

𝑎 → 𝛼

mass

𝑚 → 𝐼 moment of inertia

force

𝐹 → 𝜏 torque

linear momentum

𝑝 → 𝐿 angular momentum

Counterclockwise is…

positive for 𝜃, 𝜔, 𝛼, and 𝜏

Clockwise is…

negative for 𝜃, 𝜔, 𝛼, and 𝜏

Relating linear quantities to angular quantities x =

x = 𝑥 = 𝑟𝜃

Relating linear quantities to angular quantities v=

𝑣 = 𝑟𝜔

Relating linear quantities to angular quantities a_tangential =

𝑎_tangential = 𝑟𝛼