Download Exam 1: Equation Summary

MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01 TEAL
Fall Term 2004
Exam 1: Equation Summary
One Dimensional Kinematics:
r
r
r
r
v = dr / dt , a = dv / dt
t ′=t
vx (t ) − vx,0 =
∫
ax (t ′)dt ′
t ′=t
x(t ) − x0 =
t′=0
∫ v (t ′)dt ′
x
t′=0
Constant Acceleration:
1
x(t) = x0 + vx,0 (t − t0 ) + ax (t − t0 ) 2
2
1
y (t ) = y0 + v y,0 (t − t0 ) + a y (t − t0 ) 2
2
vx (t ) = vx,0 + ax (t − t0 )
v y (t ) = v y,0 + a y (t − t0 )
where x0 , vx,0 , y0 , v y,0 are the initial position and velocities components at t = t0
Newton’s Second Law: Force, Mass, Acceleration
r
r
F ≡ ma
r
r r
F total = F1 + F2
Fx total = max
Fy total = ma y
Fz total = maz
Newton’s Third Law:
r
r
F1,2 = −F2,1
Force Laws:
r
mm
Universal Law of Gravity: F1,2 = −G 1 22 r̂1,2 , attractive
r1,2
r
r
Gravity near surface of earth: Fgrav = mgrav g , towards earth
r
r r
Contact force: Fcontact = N + f , depends on applied forces
Static Friction: 0 ≤ f s ≤ f s,max = µ s N direction depends on applied forces
Kinetic Friction: f k = µk N opposes motion
Hooke’s Law: F = k ∆x , restoring