Section 1
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Last updated
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Date created
Mar 1, 2020
Cards (171)
Section 1
(50 cards)
Average Speed
v = d/∆t
Period of Circular Motion (UCM)
T = (2πr)/v
atto
-18
Position vector as a function of time
rf = ri + vit + ½at²
Tangential Acceleration
at = (absolulte value of) dv/dt
Position as a function of time
xf = xi + vit +½at²
Magnitude of a Vector
|A| or ||A||=√((Ax)^2+(Ay)^2)
Cartesian Coordinates in terms of polar coordinates
x = rcosθ; y = rsinθ
Cross product
The multiplication of two vectors which results in a vector. A × B=<(AyBz-ByAz),(AzBx-BzAx),(AxBy-BxAy)>
deci
-1
Centripetal Acceleration in terms of angular speed
ac = rw²
centi
-2
Centripetal Acceleration
ac =v²/r
Velocity as a function of position
vf² = vi² + 2a(xf - xi)
Translational Speed
v = rw
deka
1
Time of Flight
t = (2visinθ)/g
Average Acceleration
a = ∆v/∆t = (vf - vi)/(tf - ti)
tera
12
Average Acceleration
a= ∆v/∆t
Polar Coordinates in terms of Cartesian coordinates
tan θ = y/x; r = √(x² +y²)
Displacement
∆x = xf - xi
Instantaneous Velocity
v = lim (as ∆t→0) ∆x/∆t = dx/dt
Position as a function of velocity and time
xf = xi + ½(vi + vf)t
nano
-9
Position Vector for a particle moving in the xy plane
r = xi + yj
kilo
3
Particle under constant Velocity
xf = xi + vt
Dot product
The multiplication of two vectors which results in a scalar. A·B=|A||B|cosθ=AxBx+AyBy
mega
6
Average Velocity
v = ∆r/∆t
Displacement Vector
∆r = rf - ri
femto
-15
micro
-6
exa
18
giga
9
hecto
2
Range
R = (vi²sin2θ)/g
Average Velocity
v = ∆x/∆t
Subtracting Vectors
A - B = A + (-B)
Maximum Height
h = (vi²sin²θ)2g
milli
-3
Final velocity as a function of acceleration and time
vf = vi +at
Total Acceleration
a = ar + at
pico
-12
Instantaneous Acceleration
a = lim (as ∆t→0) ∆v/∆t = dv/dt
Instantaneous Acceleration
a = lim (as ∆t→0) ∆v/∆t = dv/dt = d²x/dt²
Instantaneous Velocity
lim (as ∆t→0) ∆r/∆t = dr/dt
Velocity vector as a function of time
vf = vi + at
peta
15
Section 2
(50 cards)
Terminal Speed (for resistive force proportional to speed squared)
v = √(2mg/DpA)
Atwood's Machine Acceleration
[(m2-m1)g]/(m1 + m2)
Isolated System
ΔEmech = 0
Perfectly Inelastic Collision Final Velocity
vf = (m₁v₁i + m₂v₂i)/(m₁ + m₂)
Weight
Fg = mg
Isolated System of Momentum/Conservation of Momentum
∆ptot = 0; ∆p1 = ∆p2
Newton's Second Law (in terms of Momentum)
∑F = d(mv)/dt = dp/dt
Tension in string of Atwood's Machine
T = m1(g+a)
Radial Acceleration
ar = -ac = - v²/r
Power
P = W/∆t
Static Friction
fs ≤ un
One dimensional elastic collision formula
v₁i - v₂i = -(v₁f - v₂f)
Work-Kinetic Energy Theorem
ΣW = ΔK
Kinetic Friction
fk = un
Newton's Second Law for Circular Motion
∑F = ma = mv²/r
Dot Product
Energy for a system
ΔEsystem = ΔK + ΔU + ΔEint
Resistive Force (when Proportional to Velocity)
R = -bv
Newton's Second Law (in terms of Force)
∑F = ma
Elastic Potential Energy
Us = ½kx^2
Linear Momentum
p = mv
Impulse of a force
I = ∫∑Fdt
Conservation of Kinetic Energy expanded
½m₁v₁i² + ½m₂v₂i² = ½m₁v₁f² +½m₂v₂f²
Work done by a spring
Situations involving Friction
ΣW(otherforces) - fkd = ΔK
Galilean Velocity Transformation
Upa = Upb + vba
Newton's Third Law
F12 = -F21
Terminal Speed (for resistive force proportional to velocity)
v = mg/b or mg - bv = 0
Newton
1 kg m/s
Newton's Second Law (in terms of acceleration)
a α ∑F/m
Work done by a constant force
W = FΔrcosθ
Kinetic Energy
K = ½mv^2
Change in Internal Energy
ΔEint = fkd (where fk stands for kinetic friction)
Gravitational Potential Energy
Ug = mgh
Conservation of Momentum expanded
m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f
Potential Energy from Conservative Forces
Conservation of Energy Equation
∆Esystem = ∑T
Impulse Momentum Theorem
∆p = I
Work done by Varying Force
Particle under a Net Force
∑F = ma
Impulse of Time Averaged Force
I = ∑Favg∆t
Resistive Force (when Proportional to Speed Squared)
R = ½DpAv²
Particle in Equilibrium
∑F = 0
Hooke's Law (Spring Force)
Fs = -kx
Change in Kinetic Energy
ΔK = Kf - Ki
Conservative force from potential energy
Work done with nonconservative forces present
ΣW(other forces) = ΔK + ΔU + ΔEint
Change in Mechanical Energy
ΔEmech = ΔK + ΔU
Instantaneous Power
P = dE/dt = dW/dt
Full Expansion of Conservation of Energy Equation
∆K + ∆U +∆Eint = W + Q + Tmw + Tmt + Tet + Ter
Section 3
(50 cards)
Angular Momentum of an Isolated System
∆L = 0 or Iw = Iw
Torque Vector Product
t = r x F
Velocity of center of mass of a system of particles
Vcm = 1/M ∑mivi = drcm/dt
Thrust
M(dv/dt) = ve(dM/dt)
Angular Displacement
∆θ = θf - θi
Elastic Collision Final Velocities
Total Kinetic Energy of a Rolling Object
K = ½Iw² + ½mv²
Instantaneous Angular Speed
w = lim (∆t→0) ∆θ/∆t = dθ/dt
Centripetal Acceleration
a = v²/r = rw²
Rectangular Plate
Icm = 1/12M(a²+b²)
Total Momentum of a system of particles
MVcm = ∑mivi
Parallel Axis Theorem
I = Icm + MD²
Hollow Cylinder
Icm = ½M(R₁² + R₂²)
Relation between Tangential velocity and Angular velocity
v = rw
Center of Mass
Rocket Propulsion
vf - vi = ve ln (Mi/Mf)
Acceleration of the center of mass of a system of particles
Macm = ∑miai = ∑Fi
Solid Sphere
Icm = 2/5MR²
Moment of Inertia
I = ∑mr² = ∫r²dm
Rotational Kinetic Energy
K = ½Iw²
Net external torque on a system based on angular momentum
∑t = dL/dt [rearranged: ∆L = ∫(∑t)dt
Newton's Second Law for a system of particles
∑Fext = Macm
Solid Cylinder or Disk
Icm = ½MR²
Total Acceleration Vector
a = r√(α² + w⁴)
Rigid Object under Net Torque
∑t = Iα
Torque (magnitude)
t = rFsin∅ = Fd
Rotational Kinematic #2
θf = θi + wit +½αt²
Magnitude of Angular Momentum
L = mvrsin∅
Rotational Kinematic #1
wf = wi + αt
Thin Spherical shell
Icm = 2/3MR²
Variation of g with altitude
g = (GM)/r² = (GM)/(R + h)²
Vector Product
C = A x B with magnitude found by C = ABsinθ
Cross product of unit vectors
i x i = j x j = k x k = 0 i x j = -j x i = k j x k = -k x j = i k x i = -i x k = j
Deformable System
∆Esystem = ∑T
Hoop or Thin Cylindrical Shell
Icm = MR²
Relation between Tangential acceleration and Angular acceleration
a = rα; (for centripetal acceleration it is a = rw²)
Average Angular Speed
w = ∆θ/∆t = (θf - θi)/(tf-ti)
Instantaneous Angular Acceleration
α = lim (∆t→0) ∆w/∆t = dw/dt
Average Angular Acceleration
α = ∆w/∆t = (wf - wi)/(tf-ti)
Rotational Form of Newton's Second Law
∑t = Iα
Newton's Law of Universal Gravitation
F = (Gm₁m₂)/r²
Arc Length
s = rθ
Rotational Kinematic #3
wf² = wi² + 2α(θf - θi)
Rotational Kinematic #4
θf = θi + ½ (wi + wf)t
Long, thin rod with rotation axis through end
I = 1/3ML²
Gravitational Field
g = F/m
Long, thin rod with rotation axis through center
Icm = 1/12ML²
Angular Momentum
L = Iw
Cross Product
The multiplication of two vectors which results in a vector. A × B=<(AyBz-ByAz),(AzBx-BzAx),(AxBy-BxAy)>
Instantaneous Angular Momentum
L = r x p
Section 4
(21 cards)