Phaidu: Notes in Physics and Mathematics
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Rotations

Homework 1

8, pg. 257
22, pg. 259
35, 39, pg. 261

Homework 2

52, pg. 262
Additional questions for 52
a) What is the acceleration of the bucket?
b) What torque does the bucket apply to the wheel?
c) At what time is the bucket at \(4 \textrm{m}\)?
d) What is the angular momentum at the time calculated in part c)?
e) Verify \(\tau=\frac{\Delta L}{\Delta t}\)
54, 56, 61, pg. 263

Simple Harmonic Motion

Homework 3

2, 4, 6, 8, pg. 451
10, 12, pg. 452
1, 2, 7, 8, 11, 12, pg. 490
13, 14, pg. 491

Waves

Coming Soon!

Coulomb's Law

Coming Soon!

Circuits

Coming Soon!

Course Resources

Extra Credit Assignment:

Consider a planet of mass \(6 \times 10^{24} \textrm{kg}\) and radius \(6 \times 10^3 \textrm{km}\). The density of air on this planet decays exponentially with distance from the surface with the data \(f\left(0\textrm{m}\right)=2 \textrm{kg}/ \textrm{m}^3\) and \( f\left(3000\textrm{m}\right)=\frac{4}{3} \textrm{kg}/ \textrm{m}^3\). The planet has a moon with mass \(7 \times 10^{22} \textrm{kg}\) and radius \(2 \times 10^3 \textrm{km}\). The moon travels in perfectly circular orbit around the planet with an orbital distance between the two centers of mass of \(4 \times 10^5 \textrm{km}\). On this moon there is a life time supply of sweet, sweet, moon cheddar. You want to fire a rocket at the moon. The day you plan to launch the moon will be directly over head. On the x-y plane put the center of mass at the point \(\left(0, 4 \times 10^5 \textrm{km}\right)\) when \(t=0 \textrm{s}\). Your space ship and you have a mass of \(1000 \textrm{kg}\) and the rockets give a force of \(3 \times 10^3 \textrm{N}\) for \(500 \textrm{s}\). Your rocket has a coefficient of drag of \(C_d = 1.33\) and its cross sectional area is \(5.00 \textrm{m}^2\). Find an from the normal vector of the planet such that you hit the moon. (5 points) If you can try to travel around the darkside of the moon, without hitting it and return to your home planet. (7 points) INCLUDE FRICTION! Submit your code, a graph of the moon's path and the rockets path, and your calculations with an explanation.

Examples: Numbers and Javascript

Alright let's try to solve this problem with numbers!


This is what a blank numbers document looks like. It's good to put your constants in their own cells. To get a cell to put in numerical numbers you can use the black "123" button to put in numbers and the black "=" button to put in equations.


Once you get everything ready you need to input the equation for acceleration. All accelerations should be from equations. Your initial position and velocity should be numbers from the problem.


The components of position and can be updated using the constant acceleration equations.


The components of velocity and can also be updated using the constant acceleration equations.


You can autofill the cells below your equation. Tap on the cell with the keyboard hidden and click on the option "Cell Actions". Then click on "Autofill Cells". This will let you autofill the cells.


Here's the cell I used to plot the surface of the Earth.


Here's my graph. You can make a graph by clicking on the "+" and navigating to the graph button.

JavaScript Link


Here's my graph using javascript and Chart.js.