PHYS101 Formula Sheet
Print, annotate both sides as you wish, and bring it to the exam. Please DO NOT TURN IN
General equations
2
Vectors a, b with interior angle θ: a · b = ab cos θ
√
b2 − 4ac
2a
|a + b|2 = a2 + b2 + 2ab cos θ
Solution to quadratic equation: ax + bx + c = 0 ⇒ x =
−b ±
Acceleration due to gravity: g = 9.81 m/s2
Kinematics
Constant acceleration: v = v0 + at
x = x0 + v0 t + 21 at2
v 2 sin 2θ
Range equation: R =
g
Reference frames: vX rel. to Y = vX rel. to Z + vZ rel. to Y
Dynamics
∆p
∆t
= µk FN
Newton’s second law: F = ma =
Force of friction: Ffr,k
Ffr,s ≤ µs FN
Circular motion and gravity
Uniform circular motion velocity: v = ωr
v2
Centripetal acceleration: a =
r 2
v
Banked curve, frictionless surface: tan θ =
rg
Gm1 m2
Force of gravity: F =
; G = 6.67×10−11 N m2 /kg2
2
r
4π 2
T2
=
Kepler’s third law:
r3
GM
Work and energy
Work: W = F · d
Kinetic energy: KE = 21 mv 2
Work-energy theorem: Wnet = ∆KE
Extended work-energy principle: Wnon−cons. = ∆KE + ∆PE
Gravitational PE: PEgrav = mgh (near earth’s surface)
Elastic PE: PEspring = 12 kx2
Hooke’s law: F = −kx
Power: power = energy/time = W/t = F · v
1
v 2 = v02 + 2a · (x − x0 )