My homework is to do some exercises on the Foucault Pendulum. I'm stuck on several of the problems. One is to find the approximate angle of rotation of the earth in one day at our latititue, which is 39.9. I found the equation n = 360 sin of latitude, but I have no idea how to use it. Another question is "What is the force that refers to the apparent force due to rotation of the earth?" Is this inertia? The last question I need help with is extremely confusing. First I have to get the time for 20 swings of the pendulum. It takes 7 seconds for one complete swing, so t = 140 seconds. Then is says, "Given the relationship, T = 2pi times the square root of l over g where l = length of pendulum, g = acceleration due to gravity = 32ft/s. Solve for l and calculate l." I don't even know where to begin for this last problem.

1. For the equation, put this into the Google Search window, Google can calculate it.

360*sin (32degrees 14minutes)

Now, instead of 32 degrees 14 minutes, put YOUR latitude in the equation.

2. What is Coriois force?

3. You really need to time 20 swings, then DIVIDE by 20 to get the period of one swing ACCURATELY.
I doubt that it will come out to 7 seconds EXACTLY.
T= 2PI sqrt (l/g)
t^2=(2PI)^2 l/g

length= t^2 * g/(2PI)^2

In the above equation(length=t^2 * g/(2PI)^2), what do the symbols ^ and * represent?

(Sorry, but this is my first semester back at college after ten years of being a stay-at-home mom, so I'm VERY rusty on a lot of areas.)

For the first problem, to find the approximate angle of rotation of the Earth in one day at your latitude, you can use the equation you mentioned: n = 360° sin(latitude). In this equation, n represents the angular rotation (in degrees) of the Earth per day at a specific latitude.

To use the equation, plug in the value for your latitude (39.9°) and solve for n:

n = 360° sin(39.9°)
n ≈ 360° * 0.63
n ≈ 226.8°

So, the approximate angle of rotation of the Earth in one day at a latitude of 39.9° is approximately 226.8°.

For the second problem, the force that refers to the apparent force due to rotation of the Earth is called the "Coriolis force." It is not inertia. The Coriolis force is an apparent force experienced by objects in motion on the rotating Earth. It deflects the object's path to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

Lastly, let's solve the third problem step by step. The given equation is T = 2π * √(l/g), where T is the time period of the pendulum (in seconds), l is the length of the pendulum (in feet), and g is the acceleration due to gravity (32 ft/s^2).

Given that the time period T is 140 seconds, and g is 32 ft/s^2, we can rearrange the equation to solve for the length of the pendulum (l):

T = 2π * √(l/g)

Squaring both sides of the equation:

T^2 = (2π)^2 * (l/g)

Dividing both sides of the equation by (2π)^2:

T^2 / (2π)^2 = l/g

Rearranging the equation:

l = g * T^2 / (2π)^2

Now we can plug in the values:

l = 32 ft/s^2 * (140 s)^2 / (2π)^2

Calculating this expression will give you the length of the pendulum (l) in feet.