Explanation Since linear momentum is p = m v , where, m is the mass of the object and v is the velocity of the object. Vector form of the above formula is: p → = m v → = m [ d x d t i ^ + d y d t j ^ + d z d t k ^ ] Because velocity in terms of the position vector is: v → = d x d t i ^ + d y d t j ^ + d z d t k ^ . The transformation of the coordinates of a point in one system to the other system is given as: x ' = x − v t , y ' = y , and z ' = z . Calculation: Taking the derivative of transformation of the coordinates, x ' = x − v t , y ' = y , and z ' = z Since, x ' = x − v t d x ′ d t = d x d t − v Similarly, d y ′ d t = d y d t and d z ′ d t = d z d t Now substitute these derivative values in equation p → = m

Modern Physics for Scientists and Engineers

4th Edition

ISBN: 9781133103721

Author: Stephen T. Thornton, Andrew Rex

Publisher: Cengage Learning

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Chapter 2, Problem 2P

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To show: Linear momentum, p=mv, has the same form p'=mv' under a Galilean transformation.

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Modern Physics for Scientists and Engineers

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Linear momentum, p = m v , has the same form p ' = m v ' under a Galilean transformation.

Solution Summary: The author explains that linear momentum, p=mv, has the same form as a Galilean transformation.

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To show: Linear momentum, p=mv, has the same form p'=mv' under a Galilean transformation.

Chapter 2 Solutions