- #1

Sahar Ali

Moved from a technical forum, so homework template missing

I have to present a topic "Good coordinates and degree of freedom" I know what are good coordinate and degree of freedom. but I will have to explain examples/question given below(from Liboff's text) I know the answer to all of them but I really do not know how to explain these how will I explain these parts to a class while presenting anyone who can give a little explanation?

For each of the following systems, specify the number of degrees of freedom and a set of good coordinates.

(a) A bead constrained to move on a closed circular loop.

(b) A bean constrained to move on the helix of constant pitch and constant radius.

(c) A particle on a right circular cylinder.

(d) A pair of scissors on a plane.

(e) A rigid rod in 3-space.

(f) A rigid cross in 3-space.

(g) A linear spring in 3-space.

(h) Any rigid body with one point fixed.

(i) A Hydrogen atom

(j) A lithium atom

(k) A compound pendulum (two pendulums attached end to end)

My answers are:

(a) The distance along loop from an arbitrary fixed point on the loop. 1 degree of freedom.

(b) The distance along helix from an arbitrary fixed point on the helix. 1 degree of freedom.

(c) Cylindrical coordinates. 2 degrees of freedom.

(d) 3 numbers to locate the center of scissors. One for angle scissors makes with the chosen axis. One for angle scissors is open. 5 degrees of freedom.

(e) 3 numbers to locate the center of a rod in space. Two numbers to orient rod in space, typically q and f.5 degrees of freedom.

(f) 3 numbers to locate a center of the rod in space. Two numbers to orient the rod in space. Two numbers to rotate about both axes in space. 6 degrees of freedom.

(g) Three numbers to locate the center of spring in space, two numbers to orient spring in space and one number for amount spring is stretched. 5 degrees of freedom.

(h) 3 numbers to locate a body in space. 2 numbers to orient body and 2 numbers about each axis of rotation. 7 degrees of freedom

(i) 3 numbers to locate proton in space. 3 numbers to locate the electron in space. 6 degrees of freedom.

(j) 3 numbers to locate the nucleus in space. 3 numbers for each electron in space. 12 degrees of freedom.

(k) 2 degrees of freedom for the first pendulum. 2 degrees of freedom for the second pendulum.

For each of the following systems, specify the number of degrees of freedom and a set of good coordinates.

(a) A bead constrained to move on a closed circular loop.

(b) A bean constrained to move on the helix of constant pitch and constant radius.

(c) A particle on a right circular cylinder.

(d) A pair of scissors on a plane.

(e) A rigid rod in 3-space.

(f) A rigid cross in 3-space.

(g) A linear spring in 3-space.

(h) Any rigid body with one point fixed.

(i) A Hydrogen atom

(j) A lithium atom

(k) A compound pendulum (two pendulums attached end to end)

My answers are:

(a) The distance along loop from an arbitrary fixed point on the loop. 1 degree of freedom.

(b) The distance along helix from an arbitrary fixed point on the helix. 1 degree of freedom.

(c) Cylindrical coordinates. 2 degrees of freedom.

(d) 3 numbers to locate the center of scissors. One for angle scissors makes with the chosen axis. One for angle scissors is open. 5 degrees of freedom.

(e) 3 numbers to locate the center of a rod in space. Two numbers to orient rod in space, typically q and f.5 degrees of freedom.

(f) 3 numbers to locate a center of the rod in space. Two numbers to orient the rod in space. Two numbers to rotate about both axes in space. 6 degrees of freedom.

(g) Three numbers to locate the center of spring in space, two numbers to orient spring in space and one number for amount spring is stretched. 5 degrees of freedom.

(h) 3 numbers to locate a body in space. 2 numbers to orient body and 2 numbers about each axis of rotation. 7 degrees of freedom

(i) 3 numbers to locate proton in space. 3 numbers to locate the electron in space. 6 degrees of freedom.

(j) 3 numbers to locate the nucleus in space. 3 numbers for each electron in space. 12 degrees of freedom.

(k) 2 degrees of freedom for the first pendulum. 2 degrees of freedom for the second pendulum.