| Quantity | Symbol | Formula |
| % Error | | % Error = ( |A-M| ) x 100 /A |
| % Uncertainty | | % Uncertainty = (Uncertainty x 100) / Measurement |
| Distance (Linear displacement) | Dx | Dx = xf - xo |
| Elapsed Time | Dt | Dt = t2 - t1 |
| Instantaneous Speed | V | V = Dd / Dt
(with t approaching zero seconds) |
| Average Speed | Vavg | Vavg = (total distance traveled)/(total elapsed time) |
| Acceleration | a | a = DV/Dt = (V2 - V1) / (t2 - t1) |
| Final Speed | V2 | V2 = V1 + aDt |
| Original Speed | V1 | V1 = V2 - aDt |
| Elapsed Time | Dt | Dt = (V2 - V1) / a |
| Kinematic Equations: | ====> | (Uniform Acceleration) |
| Final Velocity | V2 | V2 = V1 + aDt |
| Displacement | Dx | Dx = V1Dt + 0.5(aDt2) |
| Final Velocity | V2 | V22 = V12 + 2aDx |
| Displacement | Dx | Dx = 0.5(V2 + V1)Dt |
| Elapsed Time | Dt | Dt = (V2 -V1) / a |
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| Free Fall from Rest | V1 = 0.0 m/s | g = -9.8 m/s2 |
| Final Velocity | V2 | V2 = gDt |
| Displacement | Dx | Dx = 0.5(gDt2) |
| Final Velocity | V2 | V22 = 2gDx |
| Displacement | Dx | Dx = 0.5(V2 )Dt |
| Elapsed Time | Dt | Dt = (V2) / g |
| Elapsed Time | Dt | Dt = Sq. root of (2Dx/g) |
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| Dynamics | Equations | |
| Force (Newton's 2nd Law) | F = Force | F = ma |
| Friction | Ff | Ff = mFn |
| Newton's Third Law | . | FAB = -FBA |
| Weight | Fg = Fw | Fg = Fw = mg |
| Normal Force | Fn | Fn = FwCos q |
| Coefficient of Friction | m | m= Ff / Fn |
| Atwood Machine | | |
| Net Force | Fnet | Fnet = (M1- M2)g = DMg |
| 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 | DM | DM = M1- M2 |
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| Force and
on an | Acceleration
incline | |
| Angle of Incline | q | q = Sin-1(Opp/adj) |
| Acceleration (net) | a | a = gsin q |
| Accelerating Force | Fa | Fa = Fw (Sin q) |
| Normal Force | FN | FN = Fw (Cos q) |
| Vertical Acceleration | ay | ay = gsinqsinq |
| Horizontal Acceleration | ax | ax = gsinqcosq |
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| Projectile Motion |
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| (No Air Resistance!) | x = horizontal,
y = vertical | (Acceleration is in the vertical direction only!) |
| ax = 0.0 m/s2, ay = 9.8 m/s2 | Down vectors are negative in Value! | Subscript "o" means time is 0.0 seconds |
| | Up vectors are positive in value! | Formulas require ay to be positive 9.8 m/s2. (The negative value has already been entered into the formulas for acceleration!) |
| Horizontal Motion |
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| x2 = x1 + Vx1t | Vx2 = Vx1 | ax = 0.0 m/s2 |
| Vertical Motion | | |
| y2 = y1 + Vy1t - 0.5gt2 | Vy2 = Vy1 - gt | V2y2 = V2y1 - 2gDy |
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| Projectile Terms and Units: | | |
| x2 | Final Horizontal Position (meters) | Dx = x2 - x1 = Vx1t |
| x1 | Initial Horizontal Position (meters) | x1 = x2 - Vx1t |
| Vx1 | Initial Horizontal Velocity (m/s) | Vx1 = (x2 - x1) / t = Vx2 |
| Vx2 | Final Horizontal Velocity (m/s) | Vx2 = Vx1 = (x2- x1) / t |
| ax | Horizontal Acceleration (m/s2) | ax = 0.0 m/s2 |
| y2 | Final Vertical Position
(m) | Dy = y2 - y1= Vy1t - 0.5ayt2 |
| y1 | Initial Vertical Position
(m) | y1 = y2 - Vy1t + 0.5ayt2 |
| Vy1 | Initial Vertical Velocity (m/s) | Vy1 = Vy2 + ayt |
| Vy2 | Final Vertical Velocity (m/s) | Vy2 = Vy1 - ayt |
| Dy | Change in Vertical Position (m) | Dy = (y2 - y1) |
| ay | Earth's Gravitational Acceleration (m/s2) | ay = g = -9.8 m/s2 |
| t | Time of "flight" (s) | t = (Vy2 - Vy1) / ay |
| Projectile Launched | at angle q | from the horizontal |
| q | Angle of Launch from the horizontal (degrees) | q = tan -1 (Vy1 / Vx1) |
| V1 | Resultant Launch Velocity | V21 = V2y1 + V2x1 |
| Vx2 | Horizontal Launch Velocity (Component) | Vx2 = V1 . Cos q |
| Vy1 | Vertical Launch
Velocity (Component) | Vy1 = V1 . Sin q |
| R (if, y2 = y1) | Maximum Horizontal Distance traveled
(or Range) in meters | R = (V21 Sin 2q) / g |
| Momentum | (Linear) | Units: P = kg.m/s J = N.s |
| P | Momentum | P = mV |
| J | Impulse | J = F.t |
| DP | Change in Momentum | D(mV) = m(Vf - Vo) |
| J = DP | Impulse = Change in Momentum | F.t = D(mV) |
| Ptot = SmnVn | Total Initial Momentum | m1V1 + m2V2 + m3V3 + ..... |
| P'tot =SmnV'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: | Type: | Momentum Formulas |
| | Elastic Collision | m1V1 + m2V2 = m1V'1 + m2V'2 |
| | Inelastic Collision | m1V1 + m2V2 = (m1 + m2)V'f |
| | Explosion | 0 = m1V'1 + m2V'2 + m3V'3 + ..... |
| Work and Energy | (Linear Mechanical System) | |
| Work | W | W = F.d Cos q |
| Gravitational Potential Energy | Ep | Ep = Fw(h) = mgh |
| Kinetic Energy | Ek | Ek = (0.5)mv2 |
| Work | W | W = DEk + DEp |
| Work | W | W = DEk + DEp = (0.5mv2 + mgh)f - (0.5mv2 + mgh)i |
| Total Energy (system) | SE | SE = Ek + Ep + heat |
| Conservation of Energy | Initial Total Energy = (SE)i | (SE)i = (SE)f |
| Conservation of Energy | Final Total Energy = (SE)f | or (Ek + Ep + heat)i = (Ek + Ep + heat)f |
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Moderation Team
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