Physics Formulas

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