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.

**angular velocity****speed****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 particular 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 gravity and

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.**

**planetary nebula**.**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.**

**supergiant**region of the HR diagram.**supernova**explosion.**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 = 3.1t^{2} + 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

mv^{2}/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 m^{2}

What is the unit of Torque?

Newton-metres (Nm)

What is the unit of angular momentum?

kilogram metres squared per second (kg m^{2} s^{-1})

(kg m^{2} 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:

E_{p }= Vm

Derive the expression shown below for escape velocity.

E_{k} + E_{p} = 0

½mv^{2} + (-GMm/r) = 0

½mv^{2} = GMm/r

v^{2} = 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'.