Average Velocity x x0 v t t0 Instantaneous Velocity x v lim t 0 t
Kinetic Frictional Force f k k FN
Average Power W P t
PFv
_
Uniform Circular Velocity 2 r v T Centripetal Acceleration v2 ac r Centripetal Force mv 2 Fc r Velocity in Circular Orbits GM E v r
Impulse Impulse F t Linear Momentum p mv Impulse-Momentum Theorem F t mv f mv0 Center of Mass m x m2 x2 xcm 1 1 m1 m2 Velocity of Center of Mass m v m2 v2 vcm 1 1 m1 m2
Average Acceleration v v0 v a t t0 t Instantaneous Acceleration v v lim t 0 t
Kinematics/Straight Line Equations (Constant Acceleration) v v0 at
x 1 (v0 v)t 2 x v0t 1 at 2 2 2 2 v v0 2ax
Work (Done by a Constant Force) W ( F cos ) s Kinetic Energy 1 KE mv 2 2 Work-Energy Theorem 1 1 2 W KE f KE0 mv 2 mv0 f 2 2
Average Angular Velocity 0 t t0 t Average Angular Acceleration 0 t t0 t
Newton’s Second Law of Motion F a m F ma Newton’s Law of Universal Gravitation mm F G 12 2 r G 6.67259 1011 N m 2 / kg 2 Apparent Weight FN mg ma
Work Done by Gravity Tangential Velocity W (mg cos )(h0 hf ) mg (h0 h f ) VT r Gravitational Potential Energy PE mgh Work Done by NonConservative Forces
WNC ( 1 mv f 2 mgh f ) 1 mv0 2 mgh0 2 2
Tangential Acceleration aT r
Static Frictional Force f sMAX s FN