UBC Phys 117 Equation Sheet (Ives/Rieger, F15, Version 1) Vectors À= Aïî+ Ay?+A2Â Scalar (dot) Product A . B = Ax Bx + Ay By + Az Be Vector (cross) Product ? = Ax B Cx = Ay B2 - A2By Cy = Az Bx - AxBz C2 = Ax By - AyBx The cross product can also be expressed in terms of ¢, the angle between the vectors A and B: À x B= | A|B |sing. Differentiation (polynomial) d (ct ) = (cn)tn-1 Integration (polynomial, indefinite) Jcªdt =€™+1 n+1+C1 Quadratic Formula Ax2 + Bx + C = 0 Circles Area = ?r 2; Circumference = 2nr; Velocity (definition) dx (t) v(t) =' dt Acceleration (definition) a(t) =" dt dv(t) Equations of Motion for Constant Acceleration (derived) Relative Motion VCB = VCA + VAB Angular Velocity W = T 2 Uniform Circular Motion 2?? V =- T Centripetal Acceleration (derived) 3 q = = = w2r Useful Math Formulas The magnitude of a vector is given by |À| = A = Ax2 + Ay2 + A22 The dot product can also be expressed in terms of ¢, the angle between the vectors A and B: À·B= A|B | coso The direction of A x B is perpendicular to the plane of the two vectors being multiplied, and is in the direction of the following right-hand rule: curl your fingers from the direction of A to the direction of B and your thumb will point toward the direction of C' = Ax B. Integration (polynomial, definite) ct2+1 cm+1 ct" dt = n+1 n+1 Solutions of the quadratic formula: 2A Trigonometric functions x= -B + VB2 - 4AC sin0 = opposite ; hypotenuse' cos0 = adjacent hypotenuse' tan0 - opposite adjacent Kinematics Velocity is the time rate change of displacement. Acceleration is the time rate change of velocity. Vf= Vi + a(At); y = X1 + v?(At) + za(At) ; Vf2 = vi2 + 2a(Ax) Relative Motion The velocity of C relative to B is the velocity of C relative to A plus the velocity of A relative to B. Circular Motion The angular velocity (@) is given by the total angular distance the car travels (0 = 21 radians) divided by the time it takes to make one revolution (T = period). In uniform circular motion, the linear speed (v) is given by the distance traveled around the circle (2TR) divided by the period (T), the time it takes to make one revolution. An object moving along a circular path has a centripetal acceleration a, whose direction is always towards the center of the circle. Weight FG = mg Spring Force (Hooke's Law) Fspring = - kAx Kinetic Friction (definition) fk = Uk N Static Friction (definition) fs SMS N Translational Kinetic energy (definition) K = mv 2 Work (definition) S w={ $ Fds Work-Kinetic Energy Theorem ?? = WNet Relationship between potential energy and work for conservative forces AU = y - Ui =- Wc(i => f) Elastic Potential