Hi Our teacher told us the following:F = m * v² / r = m * 4 pi² /

[physwha]

hi

Our teacher told us the following:

F = m * v² / r = m * 4 pi² / T² * r

= m * 4 pi² / k * 1 / r²

= c * m / r²

F = y * mM / r2

Why is there the k and 1 / r² and later the c?

 

[vela]

Did this have to do with one object orbiting another?

 

[physwha]

Yes, it's about the Earth around the Sun for example.

PS: I now understand the c but still not k (is it the same?) and 1 / r² :S

 

[vela]

Are you familiar with the following formula?
$$T = 2\pi\sqrt{\frac{r^3}{GM}}$$where T is the time taken for one orbit, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the body being orbited.

 

[asteriatic]

Hi there,

It seems like your teacher is discussing the equation for centripetal force, which is given by F = m * v² / r. This equation relates the force (F) needed to keep an object moving in a circular path with its mass (m), velocity (v), and radius (r) of the circle. The equation can also be written as F = m * 4 pi² / T² * r, where T is the period of the circular motion. This is because the velocity (v) is equal to 2*pi*r/T, so when substituted into the original equation, it becomes F = m * 4 pi² / T² * r.

Now, let's look at the additional terms your teacher included. The k and 1/r² are likely referring to the gravitational constant (G) and the inverse square law, respectively. This is because the centripetal force equation can also be used to calculate the force of gravity between two objects. In this case, the equation becomes F = G * m * M / r², where M is the mass of the other object. The k is used to represent the gravitational constant, and the 1/r² represents the inverse square law, which states that the force between two objects is inversely proportional to the square of the distance between them.

Finally, the c represents the speed of light (c), which is a fundamental constant in physics. In this case, your teacher may be discussing the relationship between mass (m) and energy (E), which is given by the famous equation E = m * c². This equation shows that mass and energy are interchangeable, and the c in your teacher's equation may be used to represent this concept.

I hope this clarifies things for you. Keep up the good work in your science class!