Mtioj Under A Central Force

Question 1

When is F(x) a central force

Answer 1

F(x) is a central force if:
It’s always directed towards/away from origin
Magnitude depends only on r=norm(x)

Question 2

How can all central forces be written

Answer 2

All central forces can be written:

F(x)=f(r) *Er = f(r)/r * x where f(r) is a scalar function and Er=x/r

Question 3

When is central force F(x) attractive and repulsive

Answer 3

Central force F(x) is attractive towards O if f(r) < 0 and repulsive away from O if f(r) > 0

Question 4

What is newtons 2nd law

Answer 4

Newtons 2nd law is:
Force = ma
F=mx.. = F(x) = f(r)/r *x

Question 5

What equation describes motion in a plane

Answer 5

Equation that describes motion in a plane is:

Assume m=1 so x.. = f(r)/r * x

Question 6

What is angular momentum h

Answer 6

Angular momentum h is:

X x x. And if it =0 then x is parallel to x. So motion is a line.

Question 7

What are the 4 properties of motion

Answer 7

4 properties of motion are:
Equation of motion in a plane F(x) = f(r)/r * x
R^2 theta. Is constant in the plane
O allecelration in Etheta direction so r.. - h^2\r^3 = f(r)
Conservation of energy (constant)

Question 8

What is the orbit equation

Answer 8

Orbit equation is :

D^2u/drheta^2 + u = -f(u^-1)/(hu)^2

Question 9

What is solution of orbit equation

Answer 9

Solution of orbit equation is:

U(theta) = Acos(theta) + B sin(theta) + mu/h^2