6 Circular Motion Flashcards
gravitational field
A region of space where a test mass experiences a force due to the gravitational attraction of another mass
gravitational field strength
force per unit mass;
on a point mass
gravitational potential energy [J]
work done to move a body;
from infinity to a point in the gravitational field
electric potential energy [J]
work done to move the charges;
from infinite separation to their current positions in the electric field
gravitational potential
V [J kg-1]
work done per unit mass;
in bringing a point mass;
from infinity to a point in the gravitational field
electric potential, V [J C-1]
work done per unit charge;
in bringing a test charge;
from infinity to a point in the electric field
escape speed
speed of object at a planet’s surface; to escape from the gravitational field and travel to infinity
Newton’s Universal Law of Gravitation
F = GMm/r²
the force of gravity between two objects is inversely proportional the square of the separation of their centres and directly proportional to the product of their masses
describe circular motion in terms of a puck stretched by a string
The stretched string applies a centripedal force –> centripedal force is perpendicular to velocity, so there is no component of force in the direction of the velocity –> no acceleration in the direction of the velocity –> puck moves in a circle around the center with constant speed
period, T, of circular motion
time taken for the object to complete 1 rotation (2π radians)
angular displacement
∆θ = S/r
the change in angles of a body (in radians) as it rotates in a circle
angular speed
ω = ∆θ/∆t
the rate of change in angular displacement with respect to time
centripetal Force
The resultant force directed towards the centre of the circle (perpendicular to velocity) , which keeps a body in uniform circular motion
centripetal acceleration
The resultant acceleration directed towards the centre of the circle (perpendicular to velocity) when an object is moving in a circle at a constant speed
calculated the maximum speed at which a car can travel around a curved road without skidding
centripetal force = friction
mv²/r = µmg
→ v = √µgr
as you swing a ball on a string in a vertical circle,
- what is the max tension needed?
- what is the min tension needed?
- at which point is the speed of the ball fastest?
Tmax = mv²/r + mg (occurs at the bottom where T need to overcome mg AND provide centripetal force)
Tmin = mv²/r - mg (occurs at the top where mg already provides partial centripetal force and T only need to provide the rest)
since the acceleration is max at the bottom, the speed is also max at the bottom
Does the mass of a satellite affect the velocity it orbits the Earth?
No.
GMm/r² = mv²/r
the m cancels out, leaving v² = GM/r
Derive Kepler’s 3rd Law
v² = (2πr/T)² = GM/r
4π²r² /T² = GM/r
4π² r³ = GMT²
r³∝ T²
The Earth’s gravitational field always produces an … force
attractive
what are the factors that influence gravitational field strength g? derive using equation
mg = GMm/r²
cancel the m, we get
g = GM/r²
therefore, gravitational field strength g only depends upon M, the mass that causes the field, and r, the distance from the mass where we are calculating the field strength
frequency, f, of circular motion
the number of rotations in unit time (f = 1/T)
A girl is playing on a swing.
1. What is providing the centripetal force on the swing seat?
2. What is providing the centripetal force on the girl?
3. Draw a free-body diagram to show the forces acting on the girl
- tension in the swing chain
- normal reaction force from swing seat
- mg下, N斜左上，friction斜右上！！
What is providing the centripetal force on the swing seat?
a component of the normal force from the air (lift) pushing the plane’s tilted wings
What provides the centripetal force for these athletes running on a curved track?
What design features make sure that this force can be large enough for high speeds?
friction between the track and their shoes
the track needs high friction coefficient + can deform elastically
How can a beam of alpha particle be made to move in a circular path?
direct it perpendicularly across a uniform magnetic field
Does the gravitational forces between the Earth and the Moon have any noticable effect on the Earth?
tides on the oceans
Explain why it is very difficult to measure gravitational forces
gravitational forces on everyday objects are very small → technical difficulty to measure as other forces may also be acting (eg. electric, magnetic)
which equation do you use for this question:
Two planets orbit the same star at distances of 4.8 × 10^10 m and 7.9 ×10^11 m. If the first planet has a period of 200 Earth days, what is the period of the second?
Kepler’s 3rd Law:
r³/T² = constant
which equation do you use for this question: What is the required orbital speed for a satellite designed to circle the Earth at a height of 1000km?
v² = GM/r
mass of Earth
5.97 x 10^24
Calculate the distance from the centre of the Earth to a satellite which has a period of 24h.
只要跟r和T有关的都用Kepler’s 3rd Law！
r³/T² = GM/4π²
