Rotational Motion and Astrophysics Flashcards
Explain the difference between angular, tangential and centripetal acceleration.
- Angular acceleration is the rate of change of angular velocity
- Tangential acceleration is the rate of change of tangential speed
- Centripetal acceleration is the rate of change of tangential velocity- this causes the direction of the object to change and results in circular motion.
How would you find the instantaneous velocity of an object from a displacement-time graph such as this?
Take the gradient of the line.
If the graph is a curve, take the gradient of the tangent to the curve at a point.
How would you find the instantaneous acceleration of an object from a velocity-time graph such as this?
Take the gradient of the line.
If the graph is a curve, take the gradient of the tangent to the curve at a point.
How would you find the displacement of an object from a velocity-time graph such as this?
Calculate the area underneath the graph- remember to include negative values.
If the graph is a curve, the equation of the graph can be integrated to get an expression for displacement.
How would you convert an angle from degrees into radians?
Angle in radians = (2π/360) x Angle in degrees
What relationships would you use to convert between:
- Linear displacement and angular dispalcement
- Linear velocity and angular velocity
- Linear acceleration and angular acceleration
For any of these relationships, you would multiply the angular quantity by the radius of circular motion to get the linear quantity:
How is angular velocity defined in terms of angular dispalcement?
Angular velocity is defined as the rate of change of angular displacement:
How is angular acceleration defined in terms of angular velocity?
Angular acceleration is defined as the rate of change of angular velocity.
What is meant by Torque (sometimes called the moment of a force)?
Torque is the turning effect of a force on a rotating object.
What is meant by the moment of inertia of an object?
The moment of inertia of an object is a measure of its resistance to angular acceleration about a given axis.
State the law of conservation of angular momentum.
In the absence of external torques, the total angular momentum of object(s) before a collision is equal to the total angular momentum of the object(s) after the collsion.
Which two quantities does the rotatinal kinetic energy of an object depend on?
Moment of Inertia and angular velocity
What is the definition of the gravitational field strength at a point?
The force exerted per unit mass (by a gravitational field).
What is the definition of gravitational potential at a point in space?
The work done in moving a unit mass from infinity to that point in space.
At which point do both gravitational potential and gravitational potential energy have values of zero?
They both have values of zero at infinity
What is the definition of escape velocity?
The minimum velocity required to allow a mass to escape a gravitational field (and have zero gravitational potential energy)
or
The minimum velocity required to allow a mass to reach infinity
By referring to ‘frames of reference’, in which situations would
a) Special relativity
and
b) General relativity
apply?
a) Special relativity deals with motion in inertial (non-accelerating) frames of reference.
b) General relativity deals with motion in non-interial (acceelrating) frames of reference.
State what is meant by the ‘equivalence principle’.
It is impossible to tell the difference
between the effects of a uniform gravitational field and
of a constant acceleration.
Describe the effect of placing a clock at a higher altitude in a gravitational field.
The clock would run faster higher in a gravitational field.
On a spacetime diagram, what is the name given to lines representing an object’s motion?
World-lines
Describe the effect of placing a clock at a lower altitude in a gravitational field.
The clock would run slower lower in a gravitational field.
The world-lines on the following space time diagram represent the motion of different objects, A, B and C.
Describe the motion of objects A, B and C.
Object A is stationary
Object B is moving with a constant velocity
Object C is accelerating
Light or freely moving objects under the influence of gravity follow particular paths in spacetime. What are these paths called?
Geodesics
Describe the effect a mass has on spacetime.
Mass curves (or distorts) spacetime
Describe what we understand as gravity in terms of spacetime.
Gravity is caused by the curvature of spacetime. Masses follow this curvature of spacetime.
Stars can be split into what are known as ‘spectral classes’. What are the seven spectral classes?
O B A F G K M
Which of the seven spectral classes of stars is the hottest?
Spectral class O is the hottest.
Which two quantities does the Luminosity of a star depend on?
The luminosity of a star depends on it’s radius and surface temperature
When stars fuse hydrogen into helium via the proton-proton chain releasing energy (gamma rays) in the process, which two other particles are produced?
positrons and neutrinos
In this simplified Hertzsprung-Russel diagram, which types of stars can be found in areas A, B, C and D?
A- Main sequence stars
B- (Red) Giants
C- (Red) Supergiants
D- White dwarfs
Explain the stages of a low to medium mass star’s evolution from when it leaves the main sequence until its eventual fate.
- Low to medium mass stars will stop fusing H to He, their cores will contract due to gravity and will start fusing He into heavier elements such as C and O.
- They will then move into the giants region of the HR diagram.
- When He fusion stops, the outer layers drift off to become a planetary nebula.
- This leaves behind a hot, dense core known as a white dwarf.
Explain the stages of high mass star’s evolution from when it leaves the main sequence until its eventual fate.
- Higher mass stars can fuse elements in stages all the way up to Iron.
- These stars produce so much thermal pressure that they move into the supergiant region of the HR diagram.
- When fusion stops, the star’s core collapses suddenly, and rebounds outwards as a violent supernova explosion.
- The remaining core is so dense that it becomes a neutron star or black hole.
Which quantity of a star determines its ultimate fate?
Its mass.
While in the main sequence for the majority of it’s lifetime, explain how a star remains stable.
The thermal pressure outwards produced by fusion is balanced by gravitational attraction.
It is in gravitational equilibrium.
An expression for the displacement of an object with respect to time is given as
s = 3.1t2 + 4.1t + 6
Determine exprssions for the object’s velocity and acceleration.
v = 6.2t + 4.1
a = 6.2
A ball of weight W attached to a string is ‘whirling’ in a horizontal circle as shown below.
What is the centripetal force acting on the ball?
The centripetal force is suppled by the tenson, T only.
T is the only force acting into the centre.
A ball of weight W attached to a string under tension T is ‘whirling’ in a vertical circle as shown below.
Determine a relationship for the centripetal force acting on the ball:
- at the bottom.
- at the sides.
- at the top.
- Centripetal force = Tension - Weight
- Centripetal force = Tension
- Centripetal force = Tension + Weight
A ‘conical pedulum’ is shown below.
In terms of the components of tension in the string determine expressions for the:
- Centripetal force
- Weight of the ‘bob’.
- Centripetal force = T sinθ
- Weight = T cosθ
In a ‘loop the loop’ ride at a funfair, how would you determine the minimum speed required to complete a full loop?
The minimum speed required is when there is no reaction force acting on the ‘car’, so.
Centripetal force = Weight + Reaction force
simplifies to
Centripetal force = Weight
mv2/r = mg
v = √gr
What is the unit of centripetal acceleration?
ms-2
What is the unit of angular acceleration?
rad s-2
What is the unit of tangential acceleration?
ms-2
What is the unit of anguar displacement?
Radians (rad)
What is the unit of angular velocity?
rad s-1
What is the unit of moment of inertia?
kg m2
What is the unit of Torque?
Newton-metres (Nm)
What is the unit of angular momentum?
kilogram metres squared per second (kg m2 s-1)
(kg m2 rad s-1 also acceptable)
What is the unit of gravitational potential?
Joules per kilogram (J kg-1)
Shown is the relationship used to find the gravitational potential at a point in space.
How could you find the gravitational potential energy of a mass, m, at that point?
Multiply the gravitational potential by the mass:
Ep = Vm
Derive the expression shown below for escape velocity.
Ek + Ep = 0
½mv2 + (-GMm/r) = 0
½mv2 = GMm/r
v2 = 2GM/r
v = √2GM/r
What is the unit of Luminosity
Watts (W)
What is the unit of apparent brightness
Watts per square metre (Wm-2)
What is meant by the Schwarzschild radius of a black hole?
The Schwarzchild radius of a black hole is a radius of a sphere such that if all the mass of an object were compressed into it, light would not be able to escape from it’s surface, thereby forming the black hole.
The following experimental setup can be used to determine the moment of inertia of a disc which is allowed to rotate on a frictionless air bearing turntable.
Explain the measurments which will need to be taken, and how to use these to determine the moment of inertia of the disc.
Find the torque applied to the disc by using the relationship T = Fr.
Use the light gate to measure the angular acceleration of the disc.
Vary the hanging mass to vary the torque, and repeat a few times.
Plot T against α, and take the gradient of the straight line which will be equal to the monemt of inertia of the disc.
An ice skater is spinning with his arms outward as shown.
He then pulls his arms inward.
Explain what happens to his angular momentum and rotational kinetic energy.
Angular momentum constant because angular momentum is always conserved
Rotational kinetic energy increases because angular velocity increases.
What is meant by a conservative field?
The path taken between two points in the field does not affect the work done (energy) used
What is meant by the Schwarzchild radius of a black hole?
The Schwarzchild radius is the distance from the centre of a black hole to its ‘event horizon’.
Which two things does the moment of inertia of an object depend on?
- The mass of the object
- The distribution of mass around a given axis of rotation
How would you convert between
- astronmical units (AU) and metres?
- light years and metres?
- 1 AU = 1.5 x 1011 m (given in data sheet)
- 1 light year = 3 x 108 x (365.25 x 24 x 60 x 60) = 9.46 x 1015 m (NOT in data sheet!)
