Unit Kinematics Module Relative Motion and Reference Frames page 1 of 2 Understanding Relative Motion Although the physics of a system remains the same its description might change depending on the reference frame The equations rC M rC T rT M vC M vC T vT M and aC M aC T relate the motion of an object in two different reference frames M and T are the two frames and C is the object of interest A physicist is riding on a train moving at 10 m s and she observes a ball moving with a constant velocity of 2 m s Prof Pollock is standing on the ground beside the track and he observes the ball moving at 12 m s In this example a physical quantity has two different values Although the physics of the object remains the same the description changes depending on the reference frame A reference frame is a coordinate system and time scale from which physical observations are made The iguanodon is in a train that is moving northeast with a constant speed subscript T Prof Pollock subscript M and the car subscript C are not moving Using vector addition you can see that the equation rC M rC T rT M relates the position of the car in Prof Pollock s reference frame rC M to the position of the car in the train s reference frame rC T The position of the train s reference frame with respect to Prof Pollock s reference frame is rT M Taking the derivative of the position equation with respect to time results in the equation vC M vC T vT M relating the velocities in the different reference frames The equation aC M aC T equates the acceleration of the car in Prof Pollock s reference frame to the acceleration of the car in the train s reference frame Because the train is moving with constant velocity it is not accelerating www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1831 doc rev 03 29 2001 Unit Kinematics Module Relative Motion and Reference Frames page 2 of 2 Understanding Relative Motion From the bank a Prof Pollock observes a river flowing with a constant velocity of 10 m s i A boater wants to cross the river with a velocity of 10 m s j with respect to the riverbank What should the boater s velocity be with respect to the river In this example the boat subscript B is the object of interest and the river subscript R is the reference frame moving with constant velocity Prof Pollock s reference frame corresponds to the stationary reference frame subscript M Rewrite the velocity equation with the appropriate subscripts and solve for the velocity of the boat with respect to the river vB R vB M vB R vR M vB R vB M vR M 10 m s j 10 m s i 10 m s i 10 m s j www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1831 doc rev 03 29 2001
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