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Can Angles be Assigned a Dimension?

1. Some Background on Dimensional Analysis … if you are not already familiar with it. 1.1 Dimensions Dimensional Analysis is a way of analyzing physics equations that consider only the qualitative dimensions – mass, length, time, charge .. – of the quantities involved, not the values that they take in the given problem.  This is not to…

Frequently Made Errors in Vectors – Elementary Use

  A vector has magnitude and direction. Pictorially, a vector can be imagined as a location in n-dimensional space relative to some fixed origin.  The magnitude is represented by the distance from the origin to the point. In Mechanics and Introductory Physics, we mostly deal with 2- and 3-dimensional vectors. Some physical entities that behave…

Frequently Made Errors: Pseudo and Resultant Forces

  1. Real versus Fictitious Pseudo, or “fictitious“, forces can arise when a non-inertial frame of reference is used. Using a non-inertial frame makes the usual force/acceleration laws fail. Pseudo forces must be added to correct them. 2. Applied versus Resultant The applied forces on an object are the specific forces exerted on it by…

Frequently Made Errors in Mechanics: Springs

  1. Springs in Series “A spring of constant ##k_1## is connected in series with a spring of constant ##k_2##.  What is the spring constant for the composite spring?” Attempted answer: When the tension in the first spring is T, the tension in the second spring will also be T.  The two extensions will be…

Frequently Made Errors in Equation Handling

  1. Algebra versus Arithmetic When numerical values are provided as inputs in a question, it is tempting to plug these into the equations straight away.  Resist!  Create variable names for these constants and work wholly symbolically until the final step.  There are many advantages: If you make a mistake, it takes less time to…

Frequently Made Errors in Mechanics: Kinematics

    Kinematics is the subset of dynamics that only concerns itself with time, displacement, velocity, and acceleration. A problem is a kinematics problem if it involves those quantities, but consideration of masses, forces, and work are unnecessary. 1. Scalars and Vectors X  “A scalar only has magnitude while a vector has magnitude and direction”…

Frequently Made Errors in Mechanics: Moments

  The term “moment” is used in various ways in Physics and Mathematics: Given a force and a reference point, the force has a moment (or torque) about the point. A rigid body has moments of mass of various orders (zeroth, first, second..) Similarly, moments of area, and moments of statistical distributions This page only…