Download General Physics 1 Formula Sheet 2018 and more Study notes Physics in PDF only on Docsity! General Physics I Spring 2018 Formula sheet Instructions: • A formula sheet in this document will be provided for exams. You will not allowed to use any written/printed material of your own. • The whole set of equations will not be provided for mid-term exams — only the equations relevant to the material that has been covered in class up to the midterm exam. • Use this sheet as a study tool. You must know what the algebraic symbols in each equation represent. • You may write notes on the sheets and bring your own copy to recitations, but for exams you will be provided a printed sheet and no notes will be allowed. Average velocity (1D): v̄ = x2 − x1 t2 − t1 (1) Average acceleration (1D): ā = v2 − v1 t2 − t1 (2) 1D kinematics with constant acceleration: v = v0 + at (3) x = x0 + v0t+ 1 2 at2 (4) v2 = v20 + 2a(x− x0) (5) v̄ = v + v0 2 (6) General 2D kinematics equations (equations for projectile motion are obtained by setting ax = 0 and ay = −g; upward is positive for the y-axis): Horizontal component Vertical component x = x0 + v0xt+ 1 2axt 2 y = y0 + v0yt+ 1 2ayt 2 vx = v0x + axt vy = v0y + ayt v2x = v 2 0x + 2ax(x− x0) v2y = v20y + 2ay(y − y0) A vector of magnitude V making an angle θ with the x-axis has components: Vx = V cos θ Vy = V sin θ (7) The magnitude and direction (the angle θ is measured from the x-axis) of a vector with components Vx and Vy are: V = √ V 2x + V 2 y θ = tan −1 ( Vy Vx ) (8) Quadratic formula: Equation with unknown x, in the form ax2 + bx + c = 0, has solutions x = −b± √ b2 − 4ac 2a (9) 1 Name: Newton’s second law∑ ~F = m~a (10) Force of friction: Fs ≤ µsFN Fk = µkFN (11) Centripetal acceleration: aR = v2 r (12) Newton’s law of gravitation FG = G M1M2 r2 (13) Work: W = Fd cos θ (14) Kinetic energy: KE = 1 2 mv2 (15) Work-energy pinciple: Wnet = ∆KE = 1 2 mv22 − 1 2 mv21 (16) Gravitational potential energy: PEG = mgy (17) Spring potential energy: PEel = 1 2 kx2 (18) Conservation of mechanical energy: ∆KE + ∆PE = 0 (19) Force of friction: Fs ≤ µsFN Fk = µkFN (20) When non-conservative forces are present: WNC = ∆KE + ∆PE (21) Linear momentum: ~p = m~v (22) Newton’s second law:∑ ~F = m~a = ∆~p ∆t (23) Impulse: Impulse = ~F∆t (24) Conservation of linear momentum in a col- lision of two objects: mA~vA +mB~vB = mA~v ′ A +mB~v ′ B (25) Conservation of kinetic energy (elastic col- lisions): 1 2 mAv 2 A + 1 2 mBv 2 B = 1 2 mAv ′ A 2 + 1 2 mBv ′ B 2 (26) Relative velocities after 1D elastic colli- sion: vA − vB = − ( v′A − v′B ) (27) x-component of the center of mass: xCM = mAxA +mBxB + ... mA +mB + ... (28) Conversion equations for angles: 2π rad = 360◦ = 1 rev (29) Angular velocity: ω = ∆θ ∆t (30) Angular acceleration: α = ∆ω ∆t (31) Relations between angular velocity, fre- quency and period: ω = 2πf T = 1 f (32) Kinematic equations for uniformly accel- erated rotational motion: θ = θ0 + ω0t+ 1 2 αt2 (33) ω = ω0 + αt (34) ω2 = ω20 + 2α(θ − θ0) (35) ω̄ = ω + ω0 2 (36) 2
