Circular Motion

Question 1

Angular velocity

Answer 1

w = @/t, @ = angular displacement

Question 2

Angular acceleration

Answer 2

change in velocity over time; wf - wi / t

Question 3

Average angular velocity

Answer 3

wf + wi / 2

Question 4

Relationship between linear and angular speed

Answer 4

v = rw, r= radius of speed, w = angular velocity

Question 5

How to convert from rpm to rad/s

Answer 5

Multiply by 2pii/60

Question 6

How to convert from rad/s to rpm

Answer 6

Multiply by 60/2pii

Note: Where the ‘p’ in rpm stays, there the pii stays. So if rpm comes first, 2pii is on top. If it comes second, 2pii is under.

Question 7

Gravitational force

Answer 7

GM1M2 / r^2

Question 8

Gravitational field strength

Answer 8

g = F(g) / M = GM/r^2

Question 9

Gravitational field strength for earth

Answer 9

g = GM(e) / (R(e) + h)^2

Question 10

Gravitational field potential

Answer 10

U = -GM1M2/ r

Question 11

Gravitational field potential for earth

Answer 11

U = -GM1M2/ R + h

Question 12

Centripetal force

Answer 12

F = mv^2 / r

Question 13

Centripetal velocity in planetary motion

Answer 13

v^2 = GM(e) / r(e)

Question 14

Radius of the earth above the surface of the earth

Answer 14

r = R(e) + h

Question 15

What is escape velocity?

Answer 15

It is the minimum initial speed required to set a body in motion, for which the body escapes gravitational influence or force.

Question 16

Escape velocity

Answer 16

V(esc)^2 = 2GM(e) / r(e)

Question 17

State Kepler’s laws

Answer 17

1. Each planet moves in an elliptical orbit with the Sun as the focus of the ellipse.
2. The line joining the Sun and other planets sweeps equal areas in equal times.
3. The squares of the periods if revolutions of the planets are proportional to the cubes of their mean distances from the sun.