Formulas of Motion

Linear and angular acceleration, velocity and displacement

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Linear Motion Formulas

Velocity can be expressed as (velocity = constant):

v = s / t (1a)

where

v = velocity (m/s, ft/s)

s = linear displacement (m, ft)

t = time (s)

Velocity can be expressed as (acceleration = constant):

v = V0 + a t (1b)

where

V0 = linear velocity at time zero (m/s, ft/s)

Linear displacement can be expressed as (acceleration = constant):

s = V0 t + 1/2 a t2 (1c)

Combining 1a and 1c to express velocity

v = (V02 + 2 a s)1/2 (1d)

Velocity can be expressed as (velocity variable)

v = ds / dt (1f)

where

ds = change of displacement (m, ft)

dt = change in time (s)

Acceleration can be expressed as

a = dv / dt (1g)

where

dv = change in velocity (m/s, ft/s)

Angular Motion Formulas

Angular velocity can be expressed as (angular velocity = constant):

ω = θ / t (2a)

where

ω= angular velocity (rad/s)

θ = angular displacement (rad)

t = time (s)

Angular velocity can be expressed as (angular acceleration = constant):

ω = ωo + α t (2b)

where

ωo = angular velocity at time zero (rad/s)

α = angular acceleration (rad/s2)

Angular displacement can be expressed as (angular acceleration = constant):

θ = ωo t + 1/2 α t2 (2c)

Combining 2a and 2c:

ω = (ωo2 + 2 α θ)1/2

Angular acceleration can be expressed as:

α = dω / dt = d2θ / dt2 (2d)

where

dθ = change of angular displacement (rad)

dt = change in time (s)

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Related Topics

  • Mechanics Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

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