Velocity And Acceleration

Question 1

What are speed,velocity and acceleration and what does r(t) equal

Answer 1

Speed is magnitude of velocity,Velocity is change in position with respect to time and acceleration is change in velocity.
R(t) = norm(x(t))

Question 2

What is x(t)

Answer 2

X(t) is position vector of P w.r.t time

Question 3

What is the solution to the harmonic oscillator equation x. +w^2 x=0

Answer 3

Solution to harmonic oscillator equation x.. + w^2 x=0 is:
X(t) = acos(wt) + bsin(wt)
X(t) = X0cos(wt) + V0/w sin(wt)
Periodic with period T =2pi/w

Question 4

In the right handed coordinate system, if r is constant what is x.

Answer 4

In the right handed coordinate system, if r is constant then x. = r theta. *E(theta)

Question 5

Given that E(theta), E(r) and a form a right handed system, what is E(theta)

Answer 5

E(theta) = a x E(r)

Question 6

How can velocity be calculated using cross product

Answer 6

Velocity can be calculated using cross product by:

X. = rtheta. E(theta) = theta.a x x

Question 7

What are unit vectors E(r) and E(theta) in polar coordinates

Answer 7

E(r) and E(theta) in polar coordinates are:
E(r) = cos(theta)i + sin(theta)j
E(theta) = -sin(theta)i + cos(theta)j

Question 8

What are the relationships between E(theta) and E(r)

Answer 8

Relationships between E(theta) and E(r) are:
D(E(r))/d(theta) = E(theta)
D(E(theta))/d(theta) = -E(r)

Question 9

What are the relationships between E(r). And E(theta).

Answer 9

Relationships between E(r). And E(theta). Are:
E(r). = d(E(r)/dt = theta. E(theta) (chain rule)
E(theta). = d(E(theta)/dt = -theta. E(r)

Question 10

What is x(t) in polar coordinates and what does v become

Answer 10

X(t) in polar coordinates is:
X(t) = r(t)E(r(theta(t))) = rE(r)
V becomes x. = r.E(r) + rE(r). = r.E(r) +r theta.E(theta)
If r is constant r. =0 so v= r theta. E(theta)