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qf08-s05

# qf08-s05 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Spring 2005 QUIZ 8 FORMULA SHEET Quiz Date: Friday, April 1, 2005 For motion in one dimension: v av x t Average velocity; v d x d t Instantaneous velocity; For motion in three dimensions: v d r d t ; a d v d t = d 2 r d t 2 ; r ( t 1 ) = r 0 + t 1 0 v d t ; v ( t 1 ) = v 0 + t 1 0 a d t . For constant acceleration a , if r = r 0 and v = v 0 at time t = 0, then v ( t ) = v 0 + a t r ( t ) = r 0 + v 0 t + 1 2 a t 2 . For one-dimensional motion with constant acceleration a : v 2 = v 2 0 + 2 a ( x x 0 ) . For circular motion at constant speed v : a = v 2 r , where r is the radius of the circle, and the acceleration is directed towards the center of the circle. If an object has position r and velocity v , its position and velocity relative to an observer with position r 0 and velocity v 0 are given respectively by r = r r 0 , v = v v 0 . Average velocity and acceleration are given by v average r t , a average v t .

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Mass, Acceleration, and Force: F = m a (Newton’s second law); F = GMm r 2 ˆ r (the gravitational force between two particles); F = 1 4 π 0 Qq r 2 ˆ r (the electrostatic force between two particles); F x = kx (Hooke’s law); where ˆ r is a unit vector pointing from the particle which is the source of the force, toward the particle on which the force is acting.
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qf08-s05 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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