Physics Mechanics Formula Sheet, Cheat Sheet of Mechanics

Download Physics Mechanics Formula Sheet and more Cheat Sheet Mechanics in PDF only on Docsity! Physics 313 (Mechanics) Formula sheet Motion in 1 dimension: Duration, Displacement:  x= x f −xi ,  t=t f −t i Velocity: vav=  x  t , v instantaneous(t)= dx dt Acceleration: aav= Δ v Δ t , a instantaneous(t)= dv dt ...due to gravity: g=9.81 m s2 Uniform motion: v=vav=const. , x t =x0v t Motion with constant acceleration: a=aav=const. , v t =v0a t , x t =x0v0t 1 2 a t 2 vav= v i+v f 2 , v t 2=v0 2 2 a  x Motion in 2 and 3 dimensions: Position vector r=x i y j z k Instantaneous velocity and acceleration v= d r dt a= d v dt Relative velocity of particle p relative to reference frames A and B v pB=v pAv AB “Velocity of p relative to B equals ….” Projectile motion: (motion in x and y is independent) ax=0 and a y=−g or a=g=−g j  v=g t ,  r=v0 t 1 2 g t 2 , horizontal range: R= v0 2 g sin 20 Circular motion: due to centripetal acceleration (acceleration directed towards the center) ac= v2 r , a t= d v d t , speed v= 2 r T , radius r Force, Newton's Laws: Newton's 2nd law: F⃗net=∑ i=1 n F⃗ i=m a⃗ 1Newton=1 N=1 kgm s2 Newton's 3rd law: F AB=−F BA Hooke's law: F x=−k  x for spring with spring constant k Friction: static f s s Fn directed against the direction of motion kinetic f k= k F n ,  sk ; rolling f r= r F n Center of Mass: r⃗ CM= 1 M∫ r⃗ dm , F⃗net, ext=∑i=1 n F⃗i , ext=M a⃗CM Work W =∫ 1 2 F⋅d l 1Joule=1 J=1 kg m2 s2 Power P= dW dt =F⋅v 1Watt=1 W=1 kg m2 s3 Kinetic energy K= 1 2 mv 2 W total= K Potential Energy  U=−W , dU =−F⋅d l Conservative force F x=− dU dx Energy Conservation Esys=Emech+ Etherm+Echem+Eother with Emech=K sys+U sys  E sys=E in−E out Momentum p=mv Newton's 2nd F net ext= d P sys dt Impulse I⃗ sys=∫ t i tf F⃗ sys dt=Δ p⃗ Collision: coefficient of restitution e= v recession v approach is between 0 (perf. inelastic) to 1 (elastic)