Out into space Flashcards
Describe the acceleration of an object moving in a circle
Constantly accelerating towards the centre
What is centripetal force?
The force which causes the acceleration towards the centre and keeps an object in circular motion
What direction is the centripetal force acting?
Always at right angles to the motion of the object
What is angular frequency?
measure of the rate of rotation of an object
How do you define the angle in radians?
The arc-length divided by the radius
How do you define angular velocity and what are the units?
ω = θ/t rads-1
angle/time
How is linear velocity and angular velocity related?
v = rω
r is the radius o the circle
What is frequency in terms of circular motion?
The no. of complete revolutions per second
What is the period in terms of circular motion?
The time taken for a complete revolution
How is angular velocity related to frequency and time?
ω = 2πf
ω = 2π / T
Why is an object moving with constant speed in a circular motion accelerating?
Acceleration is the rate of change of velocity and as the direction is constantly changing the velocity is changing
Whats acceleration directed towards the centre of a circle called?
centripetal acceleration
What is the equation for centripetal force and how is it derived?
F = mv2 / r
F = mω2 r
Comes from F=ma as a=v2/r or a=ω2r
What would happen to an object if the centripetal force was removed?
Would fly off at a tangent
What are the equation for centripetal acceleration?
a = v2 /r
a = ω2 r
What do masses in a gravitational field experience?
A force of attraction
What is Newton’s Law of Gravitation?
All particles with mass attract all other particles by a force called gravitation
Why is there a minus sign when calculating gravitational force?
Shows the force is attractive
What is a gravitational field?
A region where an object will experience a non-contact force
What is a uniform field?
A field that is the same everywhere
What is a point mass?
An object who’s mass is concentrated at their centre
What type of field do point masses have?
radial field
When close to the Earth’s surface why can you assume that the field is perfectly uniform?
The field lines are almost parallel and are evenly spaced
What is the equation that shows Newton’s law of gravitation?
F = GmM / r^2
What is gravitational field strength?
Force per unit mass
What does gravitational field strength depend on?
Where you are in a field
What is the equation for finding gravitational field strength?
g = Fgrav / m
( Fgrav = GmM / r2 so gravitational field strength is GM/r2 )
Is gravitational field strength a vector?
Yes it has direction - towards the centre of mass
What is another way to describe the gravitational field strength?
Acceleration due to gravity
What is the principle of the conservation of energy?
Energy cannot be created to destroyed, it can only be transferred from one form to another
What is gravitational potential energy?
The work done on an object when bringing it from infinity to a given point
What is the equation for gravitational potential energy?
Egrav = - GMm / r
What is the potential energy at infinity?
zero
Why does a mass gain potential energy when you move it away from Earth?
Because potential energy is negative so as you move it away it gains potential energy as at infinity potential energy is zero
What does the gradient at a given point show on a gravitational potential energy - r graph?
Gravitational force (gradient is steepest when distance is smallest as it is closer to the centre of mass so field lines closer together)
Why does the potential energy of a mass change as you move it between two different distances?
Work is done against the force of gravity (or work is done by the force of gravity)
What does the area under a Fgrav - r graph represent?
Gravitational potential energy
What is gravitational potential?
Potential energy per unit mass
The work done on an object per unit mass in bringing it from infinity to a given point
What is the equation for gravitational potential?
Vgrav = - GM / r
What does the gradient of a Vgrav - r graph represent?
Gravitational field strength, g
What does the area under a gravitational field strength (g) - r graph represent?
Gravitational potential (Vgrav)
What do equipotentials show?
The points in a field which all have the same field strength
What happens when you travel along a line of equipotential?
You don’t lose or gain energy (no work is done against gravity)
What is perpendicular to equipotentials?
Field lines
What is a satellite?
Any smaller mass that orbits a much larger mass
How do you find the velocity of a satellite? (what two equations do you equate)
centripetal force = mv2 / r
gravitational force = GmM / r2
∴ v = √(GM/r)
How can a mass ‘esacape’ the gravitational ‘well’ of a planet?
KE ≥ GPE
How do you derive the escape velocity?
KE ≥ GPE
1/2 mv2 ≥ GMm / r2
∴ escape velocity = √(2GM/r)
