EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
6th Edition
ISBN: 9781319321710
Author: Mosca
Publisher: VST
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Chapter 1, Problem 41P
To determine

To Show: The dimension of momentum in terms of dimensions of force and time.

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Kinetic energy K (Chapter 7) has dimensions kg m²/s². It can be written in terms of the momentum p and mass mas K = 2m Determine the proper units for momentum using dimensional analysis.
Use dimensional analysis to determine how the period T of a swinging pendulum (the elapsed time for a complete cycle of motion) depends on some, or all, of these properties: the length L of the pendulum, the mass m of the pendulum bob, and the gravitational field strength g (in m/s2). Assume that the amplitude of the swing (the maximum angle that the string makes with the vertical) has no effect on the period.
In this problem, the symbols M , L , and T represent the dimensions mass, length, and time, respectively. Consider the physical quantities m , s , r , v , a , and t with dimensions [m]=M , [s]=L , [r]=L , [v]=LT−1 , [a]=LT−2 , and [t]=T . (Here, the square bracket means “the dimensions of” so, for example, [m] represents the dimensions of the quantity m .) In each part of this problem you will be given an equation that you should assume is dimensionally consistent and must find the dimensions of the quantity on the left-hand side based on the combination of quantities on the right.   What are the dimensions of K=1/2mv^2?
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