Chapter 11 Flashcards
Converting degrees to radians
=2π/ 360 x angle in degrees
Angular speed
-The angle an object rotate through per second
Angular speed is defined as…
angle ÷ time
ω = θ ÷ t
Units for angular speed =
radians per second => rads^-1
Equation for linear speed using radius and angular speed?
v = rω
Or v= 2πr/ T
Circular motion: frequency and period
-Frequency is the number of revolutions per second (revs^-1)
Equations for omega ω
ω= 2πf or ω= 2π/ T
Centripetal acceleration
- An object moving in a circular path at a constant speed is accelerating because it is changing direction
- The acceleration is always directed towards the centre of the circle
Equations for acceleration involving velocity, radius and omega
a = v^2/ r
a = ω^2r
Centripetal force
-If there is a centripetal acceleration, there must be a centripetal force acting towards the centre of the circle
Centripetal force: equations
F = mv^2/ r
F= mω^2r
If you remove the centripetal force…
The object would fly off at a tangent
Keplers rules
1-A planet moves in an ellipse with the sun at one focus
2-The line fromt he sun to the planet sweeps out equal areas in equal times
3-Square of orbital time is proportional to cube of orbital radius. T^2 ∝ r^3
How does an object move in a circular path?
-To make an object move in a circular path, a force must act perpendicular to velocity
Where does acceleration act?
Acceleration acts towards the centre of velocity
Where does centripetal force act?
- Force always acts at right angles to displacement along a circular path
- Perpendicular to velocity
No work is done when…
A force on a body acts perpendicular to its motion
When is the gravitational force the strongest on a planet?
-When it is closest to the sun
Working out the arc length between two points on a circular object using speed
= 2vsinθ/ t
and if t= 2θr/v
then => (v^2/r)x(sinθ/θ)
Expressed by words, what is the gravitational law?
all the particles in the universe attract all other particles
Expressed by an equation, what is the gravitational law?
F ∝ m1m2/ r^2
Gravitational force equation
F = -Gm1m2/ r^2
Equation for acceleration in a circle
a = v^2/ r inverse square law
Where does the minus sign come from in the equation for the gravitational force?
The minus sign says that the force is always attractive
The minus sign indicates that the force acts towards the mass M