classical dynamics

Question 1

When is a force field conservative?

Answer 1

1) A force field F is conservative if the work done is independent of the path taken between two points.

2) Equivalently: ∮𝐹⋅𝑑𝑟=0 for any closed loop.

Question 2

how do we check if this force field is conservative

Answer 2

∇ × F = 0 -> (the curl needs to be zero)
Then a potential energy function 𝑉 exists such that

𝐹 = −∇𝑉

Question 3

what remains constant in circular motion

Answer 3

r - the radius

Question 4

what is dr/dt where r = |r|

Answer 4

0

Question 5

what about the position vector r , is that constant, if not why

Answer 5

It depends on t

Question 6

if F = 0, what is conserved

Answer 6

momentum (p)

Question 7

if torque = 0 what is conserved

Answer 7

angular momentum (L)

Question 8

true or false: The total energy of a conserved system is conserved, i.e. constant

Answer 8

fax (True)

Question 9

jus run me through the properties of the vector product

Answer 9

anti symmetry: (v x w) = - (w x v)

orthogonality: v * (v x w) = w * (v x w)

Question 10

if a force is conservative what else is conserved

Answer 10

total energy (E)