AP Physics C Mech final

Center of mass of a system of two particles:

Xcm = (x1m1+x2m2)/(m1+m2)

Center of mass of a group of particles

Xcm = sum(mr)/sum(m)

Cener of mass beyond a linear sysem

solve in component form

Momentum formula

p = mv, delt p = m delt v, p = Ft (If force does not change)

Newton’s second law in terms of momentum

sum(F) = dp/dt.

Impulse

The change in momentum, J = dp = int(F)dt

Law of conservation of momentum

Momentum never changes, if KE is conserved elastic, if KE not conserved inelastic, perfectly inelastic means objects stick together afterwards.

How to calculae theta in uniform circular motion

theta = distance traveled on perimeter / radius of circle

How to calculae period in uniform circular motion

T = 2pi/w

How to calculate tangential (instantaneous) velocity in uniform circular motion

v = rw

How to calculate tangential acceleration in uniform circular motion

a = r alpha

angular motion kinematics equations

The same as linear just swap the variables

Centripetal acceleration

always points towards the center, a = v²/r

Centripetal force

Always points towards the center, maintains uniform circular motion, Fc = mv²/r

rotational kinetic energy

Krot = 1/2Iw^2²

torque

rotational force basically, t = rFsin(theta) or t = Ia

Simple harmonic motion position formula

x(t) = magnitude * cos( wt + shitf), period is T = 2pi/w

Spring period length

T = 2pisqrt(m/k)

Pendulum period length

T = 2pisqrt(l/g)

Universal Law of Gravitation

F = Gm1m2/r²

gravitational field strength/acceleration due to gravity

g = GM/r²

Gravitational Potential Energy

U = -GMm/r

Speed of orbiting Satellite

v² = gR²/r

Total Mechanical Energy in a system involving planets/sattelites

E = -GMm/2r

Escape Velocity

sqrt(2GM/r)

Kepler’s third law

R³/T² = a constant value