formulae of mechanics........plzzzz see.................!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!   12 Nickels awarded! Tagged with:  academic    posted on 23 Aug 2007 12:23:11 IST
Formulas  and Symbols of mechanics........!!!!!!!!!!!!! Physics I          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 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)        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 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       Projectile Motion (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 x2 = x1 + Vx1t Vx2 = Vx1 ax = 0.0 m/s2 Vertical Motion       y2 = y1 + Vy1t - 0.5gt2 Vy2 = Vy1 - gt V2y2  =  V2y1 - 2gDy           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	About the Author: nivedh_89 (4573) Blazing goIITian  835   1  [1036 rates] total posts: 1237     Offline
this article: 27 points  (with 5    in 6 votes )   [?]   You have to be logged on to rate
comment by ac    (posted on 23 Aug 2007 12:57:58 IST) This list comes in handy for revision, will help people. Your articles are adding value to this community. Try and put in some of the conclusions/notes you have made about topics during the course of your study. These are generally not found in any book, and help a lot. Keep writing!! AC (IIT Delhi alumnus, forum expert)
comment by nivedh_89    (posted on 23 Aug 2007 13:40:52 IST) thank u SIR...............................!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
comment by cutepooja    (posted on 23 Aug 2007 14:31:36 IST) gr8
comment by swashata4iit    (posted on 23 Aug 2007 14:39:38 IST) This is really nice. keep it up. But do remember dat it is time consuming
comment by kamalasai    (posted on 23 Aug 2007 15:44:27 IST) its good.........
comment by nivedh_89    (posted on 23 Aug 2007 17:14:58 IST) thanx.............................!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
comment by rini    (posted on 23 Aug 2007 17:27:20 IST) gud..
comment by rasheed786    (posted on 23 Aug 2007 18:12:28 IST) sir can u plz post such imp formulas for other topics? specially of 12
comment by nivedh_89    (posted on 23 Aug 2007 18:15:00 IST) like for wch topics.............................................????????? i hav already posted some for integration,conics,etc..................!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
comment by apurviitjee2008    (posted on 23 Aug 2007 18:52:40 IST) very good concise formula sheet
comment by dream_iit    (posted on 23 Aug 2007 20:59:09 IST) hey , can u post shortcuts , these we can find in some books , but u collected all here , so thank u , but can u post some shortcuts....it will b a lot help... and yes , how many formulas can we learn , so its also a burden coz syllabus is also not less , vo toh finish hota nahi hai.... so if u post some shrtcts i will b helpful
comment by nivedh_89    (posted on 25 Aug 2007 14:47:22 IST) i will try.......................!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
comment by nivedh_89    (posted on 27 Aug 2007 12:20:51 IST) neways thanx for the rates.........!!!!!!!

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