Physics Formula Sheet Projectile Motion Formulas x f =x 0 + v 0 t+ 1 2 at 2 v f =v 0 + at v f 2 =v 0 2 +2 aΔx v 0x =v 0 cos ( α o ) v 0y =v 0 sin ( α o ) x= ( v 0 cos ( α o )) t y= ( v 0 sin ( α o )) t− 1 2 gt 2 v x =v 0 cos ( α o ) v y =v 0 sin ( α o ) −¿ Dot Product A∗B=¿ A ∨¿ B∨cosθ Uniform Circular Motion a rad = v 2 R a rad = 4 π 2 R T 2 v= 2 πR T Gravity a=−g g=9.8 m / s 2 Relative Motion v P/ A = v P / B + v B / A Conservation of Energy K i +U i + W NC =K f +U f Total Mechanical Energy E= ∑ U+ ∑ K Energy of a Spring W spring =U elas = 1 2 kx 2 F ( x) = −dU dx ⟹ F=−kx Work and Power W =Fd {cos ( θ ) } P= W t = dW dt =Fv =τω Gravitational Potential Energy U grav =mgh Distance (Time and Two Velocities Known) d= v f −v i 2 t Center of Mass x cm = m 1 x 1 +m 2 x 2 +… m 1 +m 2 +… y cm = m 1 x 1 +m 2 y 2 +… m 1 +m 2 +… v cm = m 1 v 1 +m 2 v 2 +… m 1 +m 2 +… Power: Watts = Joules second Energy in Rotational Motion K= 1 2 Iω 2 Torque ∑ τ=Iα I= ∑ mr 2 τ= r× F=rmvsin( θ) Keep in mind: | a b c d | =ad −bc a× b= | ^ i ^ j ^ k a 1 a 2 a 3 b 1 b 2 b 3 | = | a 2 a 3 b 2 b 3 | ^ i− | a 1 a 3 b 1 b 3 | ^ j + | a 1 a 2 b 1 b 2 | ^ k Rotation Motion Equations θ f =θ i +ω i t+ 1 2 α 2 ω f =ω i +αt ω f 2 =ω i 2 + 2 α ( Δθ) α is the rotational acceleration ω= v r a trans =rα Momentum p=m v Impulse Momentum change during time interval J=Δ p= p 2 − p 1 = ∫ F ( x ) dx F(x) is a function of force in terms of x. Conservation of Momentum If the vector sum of external forces is zero, the total momentum of the system is Angular Momentum L= r× p= r×m v=rmvsin ( θ ) L=Iω Conservation of Angular Momentum Angular momentum is conserved when there is no net torque. L 0 =L f