Physics Formulas and Symbols Physics I Quantity
Symbol
% Error
Formula % Error = ( |A-M| ) x 100 /A % Uncertainty = (Uncertainty x 100) / Measurement
% Uncertainty Distance (Linear displacement)
∆x
∆x = xf - xo
Elapsed Time
∆t
∆t = t2 - t1
Instantaneous Speed
V
V = ∆d / ∆t (with t approaching zero seconds)
Average Speed
Vavg
Vavg = (total distance traveled)/(total elapsed time)
Acceleration
a
a = ∆V/∆t = (V2 - V1) / (t2 - t1)
Final Speed
V2
V2 = V1 + a∆t
Original Speed
V1
V1 = V2 - a∆t
Elapsed Time
∆t
∆t = (V2 - V1) / a
Kinematic Equations:
====>
(Uniform Acceleration)
Final Velocity
V2
V2 = V1 + a∆t
Displacement
∆x
∆x = V1∆t + 0.5(a∆t2)
Final Velocity
V2
V22 = V12 + 2a∆x
Displacement
∆x
∆x = 0.5(V2 + V1)∆t
Elapsed Time
∆t
∆t = (V2 -V1) / a
Free Fall from Rest
V1 = 0.0 m/s
g = -9.8 m/s2
Final Velocity
V2
V2 = g∆t
Displacement
∆x
∆x = 0.5(g∆t2)
Final Velocity
V2
V22 = 2g∆x
Displacement
∆x
∆x = 0.5(V2 )∆t
Elapsed Time
∆t
∆t = (V2) / g
Elapsed Time
∆t
∆t = Sq. root of (2∆x/g)
Dynamics
Equations
Force (Newton's 2nd Law)
F = Force
F = ma
Friction
Ff
Ff = µFn
Newton's Third Law
.
FAB = -FBA
Weight
Fg = Fw
Fg = Fw = mg
Normal Force
Fn
Coefficient of Friction
µ
µ= Ff / Fn
Net Force
Fnet
Fnet = (M1- M2)g = ∆Mg
Acceleration
a
a = (Fnet ) / (M1+ M2)
Net Force
Fnet
Fnet = (M1+ M2)a
Mass 1
M1
.
Mass 2
M2
.
Total Mass
Mtot
Mtot = M1+ M2
Mass Difference
∆M
∆M = M1- M2
Fn = FwCos θ
Atwood Machine
Force and Acceleration on an incline
θ
= Sin-1(Opp/adj)
Angle of Incline
θ
Acceleration (net)
a
a = gsin θ
Accelerating Force
Fa
Fa = Fw (Sin θ)
Normal Force
FN
FN = Fw (Cos θ)
Vertical Acceleration
ay
ay = gsinθsinθ
Horizontal Acceleration
ax
ax = gsinθcosθ
x = horizontal, y = vertical Down vectors are negative in Value!
(Acceleration is in the vertical direction only!) Subscript "o" means time is 0.0 seconds Formulas require ay to be positive 9.8 m/s2. (The negative value has already been entered into the formulas for acceleration!)
Projectile Motion (No Air Resistance!) ax = 0.0 m/s2, ay = 9.8 m/s2
Up vectors are positive in value! Horizontal Motion
x2 = x1 + Vx1t
Vx2 = Vx1
ax = 0.0 m/s2
Vy2 = Vy1 - gt
V2y2 = V2y1 - 2g∆y
Final Horizontal Position (meters) Initial Horizontal Position (meters) Initial Horizontal Velocity (m/s) Final Horizontal Velocity (m/s)
∆x = x2 - x1 = Vx1t
Vertical Motion
y2 = y1 + Vy1t - 0.5gt2 Projectile Terms and Units: x2 x1 Vx1 Vx2
x1 = x2 - Vx1t Vx1 = (x2 - x1) / t = Vx2 Vx2 = Vx1 = (x2- x1) / t
ax y2 y1 Vy1 Vy2 ∆y ay
Horizontal Acceleration (m/s2) Final Vertical Position (m) Initial Vertical Position (m) Initial Vertical Velocity (m/s) Final Vertical Velocity (m/s) Change in Vertical Position (m) Earth's Gravitational Acceleration (m/s2)
t
Time of "flight" (s)
Projectile Launched
at angle θ
θ V1 Vx2 Vy1 R (if, y2 = y1)
Momentum
Angle of Launch from the horizontal (degrees) Resultant Launch Velocity Horizontal Launch Velocity (Component) Vertical Launch Velocity (Component) Maximum Horizontal Distance traveled (or Range) in meters
(Linear)
ax = 0.0 m/s2 ∆y = y2 - y1= Vy1t - 0.5ayt2 y1 = y2 - Vy1t + 0.5ayt2 Vy1 = Vy2 + ayt Vy2 = Vy1 - ayt ∆y = (y2 - y1)
ay = g = -9.8 m/s2 t = (Vy2 - Vy1) / ay
from the horizontal θ = tan -1 (Vy1 / Vx1) V21 = V2y1 + V2x1 Vx2 = V1 . Cos θ Vy1 = V1 . Sin θ R = (V21 Sin 2θ) / g Units:
P = kg.m/s
J = N.s
P J
Momentum Impulse
P = mV J = F.t
∆P
Change in Momentum
∆(mV) = m(Vf - Vo)
J = ∆P
Impulse = Change in Momentum
F.t = ∆(mV)
Ptot = ΣmnVn
Total Initial Momentum
m1V1 + m2V2 + m3V3 + .....
P'tot =ΣmnV'n
Total Final Momentum
m1V'1 + m2V'2 + m3V'3 + .....
Ptot =P'tot
Conservation of Momentum
m1V1 + m2V2 + m3V3 + ..... = m1V'1 + m2V'2 + m3V'3 + .....
Explosions and Collisions:
Work and Energy
Type:
Momentum Formulas
Elastic Collision Inelastic Collision Explosion
m1V1 + m2V2 = m1V'1 + m2V'2 m1V1 + m2V2 = (m1 + m2)V'f 0 = m1V'1 + m2V'2 + m3V'3 + .....
(Linear Mechanical System) W
W = F.d Cos θ
Ep
Ep = Fw(h) = mgh
Ek
Ek = (0.5)mv2
Work
W
W = ∆Ek + ∆Ep
Work
W
W = ∆Ek + ∆Ep = (0.5mv2 + mgh)f (0.5mv2 + mgh)i
Total Energy (system)
ΣE
ΣE = Ek + Ep + heat
Conservation of Energy
Initial Total Energy = (Σ E)i
(ΣE)i = (ΣE)f
Work Gravitational Potential Energy Kinetic Energy
Conservation of Energy Final Total Energy = (ΣE)f
or (Ek + Ep + heat)i = (Ek + Ep + heat)f