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KA AH Physics > Rotational Motion and Astrophysics > Flashcards

Rotational Motion and Astrophysics Flashcards

1
Q

Explain the difference between angular, tangential and centripetal acceleration.

A
  • 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.
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2
Q

How would you find the instantaneous velocity of an object from a displacement-time graph such as this?

A

Take the gradient of the line.

If the graph is a curve, take the gradient of the tangent to the curve at a point.

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3
Q

How would you find the instantaneous acceleration of an object from a velocity-time graph such as this?

A

Take the gradient of the line.

If the graph is a curve, take the gradient of the tangent to the curve at a point.

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4
Q

How would you find the displacement of an object from a velocity-time graph such as this?

A

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.

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5
Q

How would you convert an angle from degrees into radians?

A

Angle in radians = (2π/360) x Angle in degrees

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6
Q

What relationships would you use to convert between:

  1. Linear displacement and angular dispalcement
  2. Linear velocity and angular velocity
  3. Linear acceleration and angular acceleration
A

For any of these relationships, you would multiply the angular quantity by the radius of circular motion to get the linear quantity:

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7
Q

How is angular velocity defined in terms of angular dispalcement?

A

Angular velocity is defined as the rate of change of angular displacement:

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8
Q

How is angular acceleration defined in terms of angular velocity?

A

Angular acceleration is defined as the rate of change of angular velocity.

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9
Q

What is meant by Torque (sometimes called the moment of a force)?

A

Torque is the turning effect of a force on a rotating object.

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10
Q

What is meant by the moment of inertia of an object?

A

The moment of inertia of an object is a measure of its resistance to angular acceleration about a given axis.

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11
Q

State the law of conservation of angular momentum.

A

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.

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12
Q

Which two quantities does the rotatinal kinetic energy of an object depend on?

A

Moment of Inertia and angular velocity

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13
Q

What is the definition of the gravitational field strength at a point?

A

The force exerted per unit mass (by a gravitational field).

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14
Q

What is the definition of gravitational potential at a point in space?

A

The work done in moving a unit mass from infinity to that point in space.

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15
Q

At which point do both gravitational potential and gravitational potential energy have values of zero?

A

They both have values of zero at infinity

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16
Q

What is the definition of escape velocity?

A

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

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17
Q

By referring to ‘frames of reference’, in which situations would

a) Special relativity

and

b) General relativity

apply?

A

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.

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18
Q

State what is meant by the ‘equivalence principle’.

A

It is impossible to tell the difference
between the effects of a uniform gravitational field and
of a constant acceleration.

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19
Q

Describe the effect of placing a clock at a higher altitude in a gravitational field.

A

The clock would run faster higher in a gravitational field.

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20
Q

On a spacetime diagram, what is the name given to lines representing an object’s motion?

A

World-lines

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21
Q

Describe the effect of placing a clock at a lower altitude in a gravitational field.

A

The clock would run slower lower in a gravitational field.

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22
Q

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.

A

Object A is stationary

Object B is moving with a constant velocity

Object C is accelerating

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23
Q

Light or freely moving objects under the influence of gravity follow particular paths in spacetime. What are these paths called?

A

Geodesics

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24
Q

Describe the effect a mass has on spacetime.

A

Mass curves (or distorts) spacetime

25
Q

Describe what we understand as gravity in terms of spacetime.

A

Gravity is caused by the curvature of spacetime. Masses follow this curvature of spacetime.

26
Q

Stars can be split into what are known as ‘spectral classes’. What are the seven spectral classes?

A

O B A F G K M

27
Q

Which of the seven spectral classes of stars is the hottest?

A

Spectral class O is the hottest.

28
Q

Which two quantities does the Luminosity of a star depend on?

A

The luminosity of a star depends on it’s radius and surface temperature

29
Q

When stars fuse hydrogen into helium via the proton-proton chain releasing energy (gamma rays) in the process, which two other particles are produced?

A

positrons and neutrinos

30
Q

In this simplified Hertzsprung-Russel diagram, which types of stars can be found in areas A, B, C and D?

A

A- Main sequence stars

B- (Red) Giants

C- (Red) Supergiants

D- White dwarfs

31
Q

Explain the stages of a low to medium mass star’s evolution from when it leaves the main sequence until its eventual fate.

A
  • 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.
32
Q

Explain the stages of high mass star’s evolution from when it leaves the main sequence until its eventual fate.

A
  • 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.
33
Q

Which quantity of a star determines its ultimate fate?

A

Its mass.

34
Q

While in the main sequence for the majority of it’s lifetime, explain how a star remains stable.

A

The thermal pressure outwards produced by fusion is balanced by gravitational attraction.

It is in gravitational equilibrium.

35
Q

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.

A

v = 6.2t + 4.1

a = 6.2

36
Q

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?

A

The centripetal force is suppled by the tenson, T only.

T is the only force acting into the centre.

37
Q

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:

  1. at the bottom.
  2. at the sides.
  3. at the top.
A
  1. Centripetal force = Tension - Weight
  2. Centripetal force = Tension
  3. Centripetal force = Tension + Weight
38
Q

A ‘conical pedulum’ is shown below.

In terms of the components of tension in the string determine expressions for the:

  1. Centripetal force
  2. Weight of the ‘bob’.
A
  1. Centripetal force = T sinθ
  2. Weight = T cosθ
39
Q

In a ‘loop the loop’ ride at a funfair, how would you determine the minimum speed required to complete a full loop?

A

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

40
Q

What is the unit of centripetal acceleration?

A

ms-2

41
Q

What is the unit of angular acceleration?

A

rad s-2

42
Q

What is the unit of tangential acceleration?

A

ms-2

43
Q

What is the unit of anguar displacement?

A

Radians (rad)

44
Q

What is the unit of angular velocity?

A

rad s-1

45
Q

What is the unit of moment of inertia?

A

kg m2

46
Q

What is the unit of Torque?

A

Newton-metres (Nm)

47
Q

What is the unit of angular momentum?

A

kilogram metres squared per second (kg m2 s-1)

(kg m2 rad s-1 also acceptable)

48
Q

What is the unit of gravitational potential?

A

Joules per kilogram (J kg-1)

49
Q

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?

A

Multiply the gravitational potential by the mass:

Ep = Vm

50
Q

Derive the expression shown below for escape velocity.

A

Ek + Ep = 0

½mv2 + (-GMm/r) = 0

½mv2 = GMm/r

v2 = 2GM/r

v = √2GM/r

51
Q

What is the unit of Luminosity

A

Watts (W)

52
Q

What is the unit of apparent brightness

A

Watts per square metre (Wm-2)

53
Q

What is meant by the Schwarzschild radius of a black hole?

A

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.

54
Q

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.

A

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.

55
Q

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.

A

Angular momentum constant because angular momentum is always conserved

Rotational kinetic energy increases because angular velocity increases.

56
Q

What is meant by a conservative field?

A

The path taken between two points in the field does not affect the work done (energy) used

57
Q

What is meant by the Schwarzchild radius of a black hole?

A

The Schwarzchild radius is the distance from the centre of a black hole to its ‘event horizon’.

58
Q

Which two things does the moment of inertia of an object depend on?

A
  1. The mass of the object
  2. The distribution of mass around a given axis of rotation
59
Q

How would you convert between

  1. astronmical units (AU) and metres?
  2. light years and metres?
A
  1. 1 AU = 1.5 x 1011 m (given in data sheet)
  2. 1 light year = 3 x 108 x (365.25 x 24 x 60 x 60) = 9.46 x 1015 m (NOT in data sheet!)

KA AH Physics (4 decks)

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