ap physics m formulas

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36 Terms

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time independent kinematics equation

vf2 = vo2 + 2ax

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net force (Newton’s second law)

F = ma

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force in terms of momentum (Newton’s 2nd law as a derivative)

F = dp/dt

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force in terms of potential energy

F = -dU/dx

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impulse

J = ∫F dt

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definition of momentum

p = mV

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impulse - momentum theroem

J = ∆p

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force of friction

Fƒ ≤ µFN

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work done by a constant force (dot product)

W = F * d

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work done by a variable force (integral)

W = ∫F * ds

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kinetic energy (linear)

EK = (1/2)mv2

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work - energy theorem

Wnet = ∆Ek

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power (as a rate of change)

P = dW/dt

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power (dot product)

P = F * v

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centripetal acceleration

ac = v²/r = ω2r

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torque (cross product)

τ = r x F

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Newton’s second law for rotation (torque and angular acceleration)

τ = Iα

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moment of inertia of a collection of particles (no integral)

I = ∑miri2

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parallel axis theorem

I = Icom + mh²

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rotational inertia of a rod about an axis through its center

Irod = (mℓ2)/12

/ ℓ is not a vector

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angular momentum of a moving particle (cross product)

ℓ = r x p

/ ℓ is a vector

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angular momentum of a rigid rotation body (rotational inertia)

L = Iω

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position of a center of mass for a collection of particles (sigma notation)

rcom = (∑miri)/M

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conversion between linear and angular velocity (no slip)

ω x r = V → V = rω

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rotational kinetic energy

Ek = (1/2)Iω2

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force of a spring (Hooke’s law)

F = -kx

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potential energy of a spring

Uspring = (1/2)kx2

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period of a spring mass system

T = 2π √(m/k)

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angular frequency of a general pendulum

ω = √(MgD/t)

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period of a simple pendulum

T = 2π √(ℓ/g)

/ ℓ is not a vector

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relationships between period, frequency, and angular frequency

1/T = ƒ = ω/(2π)

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Newton’s law of gravitation

FG = (Gm1m2)/r²

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gravitational potential energy

UG = (-Gm1m2)/r

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total mechanical energy of an object in circular orbit

Utotal = (-Gm1m2)/2r

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Kepler’s 3rd law

2)/(r3) = (4π2)/(GMs)

/ note: r is average of rmin and rmax

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escape velocity

vescape = √((2GMe)/Re) = √(2Reg)