AP Physics C

Kinematic Equation without x

V = at + Vo

Kinematic Equation without v

x = (1/2)at² + Vot + Xo

Kinematic Equation without t

V² = Vo² + 2a(delta x)

Kinematic Equation without a

x = (1/2)t(V+Vo)

Center of Mass (non-integral form)

Xcm = 1/M * the sum of (mi * xi)

Center of mass (integral form)

Rcm = 1/M integral of r * dm

Equation of Lamda

M/V

What to substitute for dm in the Rcm integral equation

dm = lamda* dx

Equation for a in a half-atwood machine

a = ((m2g)/(m2 + m1))

Formula for Fg

G (m1*m2)/(r²)

g for planets

GM/r²

Gravity when inside a planet

Fg = krpartial

Fs (Hooke’s Law)

-k (delta x)

Keq for Parallel Springs

the sum of the ks

Keq for series springs

the sum of 1/k

Centripetal Acceleration

v²/r

Minimum speed to maintain a vertical circle

Vmin = square root of gr

Equation for work

Force * Distance

Units of Work

Joules

Integral of Force

Work

Derivative of Work

Force

Kinetic Energy Formula

½ mv²

Potential Gravitational Energy

mg (delta h)

Potential Spring Energy

½ k (delta x)²

Conservative Force

Path-independent forces like field forces

Power Formula

Delta E/Delta t OR Force * Velocity

Units for Power

Watts

Negative Work done by a field equals

a positive change in gravitational potential energy

Linear Momentum Formula

m * v

Units for linear momentum

kgm/s

Newton’s second law for momentum

The sum of the forces = delta p/delta t

Impulse

F * delta t

Units for Impulse

Ns

Elastic Collision

A collision where energy and kinetic energy is preserved

Inelastic collision

A collision where momentum is conserved but kinetic energy isn’t, objects stick together if perfectly inelastic

Formula for Torque

r * F

Units of Torque

m * N

Formula for Rotational Inertia

Sum of m * r²

Forumla for rotational inertia of a bar rotating around it’s middle

I = (ML²)/12

Formula for rotational inertia of a bar rotating around it’s end

I = (ML²)/3

Rotational Inertia of a hoop

I = Mr²

Rotational Inertia of a cyliner

I = ½ * Mr²

Rotational Inertia of a sphere

I = 2/5 * Mr²

Parallel Axis Theorem

I’ = Icm + d²

Newton’s Second Law of Rotation

The sum of the torques = I * alpha

Rotational Kinetic Energy

Ekr = ½ * I * W²

Integral of torque

Rotational Work

Angular Momentum

I Omega OR r * p

Formula for Frequancy

F = 1/t