OAT Bootcamp - Physics Equation Sheet - Complete Formula Reference for Test Preparation

OAT Bootcamp Physics Equation Sheet

LINEAR KINEMATICS

Formula Notes

Average Velocity 𝑑 vavg = velocity (units: m/s)
𝑣𝑎𝑣𝑔 = d = displacement (units: m)
𝑡
t = time (units: s)

Displacement 1 2 d = displacement (units: m)
𝑑 = 𝑣𝑖𝑡 + 2
𝑎𝑡 vi = initial velocity (units: m/s)
a = acceleration (units: m/s2)
t = time (units: s)

Final Velocity 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 vf = final velocity (units: m/s)
(Time) vi = initial velocity (units: m/s)
a = acceleration (units: m/s2)
t = time (units: s)

Final Velocity 2 2 vf = final velocity (units: m/s)
(Displacement) 𝑣𝑓 = 𝑣𝑖 + 2𝑎𝑑 vi = initial velocity (units: m/s)
a = acceleration (units: m/s2)
d = displacement (units: m)

Average Acceleration (𝑣𝑓 − 𝑣𝑖) aavg = acceleration (units: m/s2)
𝑎𝑎𝑣𝑔 = vf = final velocity (units: m/s)
𝑡 vi = initial velocity (units: m/s)
t = time (units: s)


FORCES

Formula Notes

Net Force 𝐹𝑛𝑒𝑡 = 𝑚𝑎 Fnet = net force (units: N)
m = mass (units: kg)
a = acceleration (units: m/s2)

Weight 𝐹𝑤 = 𝑚𝑔 Fw = weight (units: N)
m = mass (units: kg)
g = acceleration due to gravity (g = 10 m/s2)

Normal Force FN = normal force (units: N)
𝐹𝑁 = 𝐹𝑤𝑐𝑜𝑠(θ) Fw = weight (units: N)
m = mass (units: kg)
θ = angle between horizontal and force

Friction Force 𝐹𝑓 = µ𝐹𝑁 Ff = friction force (units: N)
FN = normal force (units: N)
µ = friction coefficient
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, GRAVITATIONAL

Formula Notes

Gravitational 𝐺𝑚1𝑚2 F = gravitational force (units: N)
Force 𝐹= G = gravity constant (G = 6.67 x 10-11 N⋅m2/kg2)
2
(Two bodies) 𝑑 m1 = mass object 1 (units: kg)
m2 = mass object 1 (units: kg)
d = distance between centers of objects (units: m)

Gravitational 𝐺𝑚 g = acceleration due to gravity (g = 10 m/s2)
Acceleration 𝑔= 2 G = gravity constant (G = 6.67 x 10-11 N⋅m2/kg2)
(One body) 𝑟 m = mass single body (units: kg)
r = radius of body (units: m)


ROTATIONAL & CIRCULAR MOTION

Formula Notes

Uniform Circular 2π𝑟 vc = velocity (units: m/s)
Motion Velocity 𝑣𝑐 = r = radius (units: m)
𝑇
T = period (units: s)

Centripetal 2 ac = centripetal acceleration (units: m/s2)
𝑣
Acceleration 𝑎𝑐 = v = velocity (units: m/s)
𝑟 r = radius (units: m)

Centripetal Force 2 Fc = centripetal force (units: N)
𝑚𝑣
𝐹𝑐 = 𝑚𝑎𝑐 = m = mass (units: kg)
𝑟 ac = centripetal acceleration (units: m/s2)
v = velocity (units m/s)
r = radius (units: m)

Torque τ=𝑟×𝐹 τ = torque vector (units: N⋅m)
r = lever arm vector (units: m)
F = force vector (units: N)
|τ| = |𝑟||𝐹|𝑠𝑖𝑛θ θ = angle between lever arm and force
Note: |x| denotes magnitude or absolute value

Linear 𝑑 = 𝑟θ d = linear displacement (units: m)
Displacement r = radius (units: m)
θ = angular displacement (units: rad)

Linear Velocity 𝑣 = 𝑟ω v = linear velocity (units: m/s)
r = radius (units: m)
ω = angular velocity (units: rad/s)

Linear 𝑎 = 𝑟α a = linear acceleration (units: m/s2)
Acceleration r = radius (units: m)
α = angular acceleration (units: rad/s2)




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