Distance-Weighted Moments: Torque, Mass, and Multipoles

All flashcards

What is a moment in physics?

A quantity formed by weighting a physical quantity by its distance, or a power of its distance, from a reference point.

How is the moment of force expressed as a vector?

$\boldsymbol{\tau}=\mathbf{r}\times\mathbf{F}$, where $\mathbf{r}$ is measured from the reference point.

What does moment of inertia measure?

Resistance to changes in rotational motion; for point masses, $I=\sum_i m_i r_i^2$.

What is angular momentum for a particle?

The cross product of position and linear momentum: $\mathbf{L}=\mathbf{r}\times\mathbf{p}$.

What does an electric dipole moment describe?

The separation and orientation of positive and negative charge.

Quiz questions

1. A force acts along the position vector from a pivot to its point of application. What is its torque about that pivot?Answer: Zero, because the force has no perpendicular lever arm.
2. If one point mass is moved to twice its original perpendicular distance from an axis, how does its contribution to moment of inertia change?Answer: It becomes four times as large.
3. How is the center of mass of a collection of point masses calculated?Answer: As the sum of each position weighted by its mass, divided by total mass.
4. Which vector expression gives a particle's angular momentum about a reference point?Answer: $\mathbf{r}\times\mathbf{p}$
5. For two equal and opposite point charges, which direction does the electric dipole moment vector point under the usual convention?Answer: From the negative charge toward the positive charge.