MORLEY SENIOR HIGH SCHOOL
YEAR 12
PHYSICS (STAGE 3)
RELATIVITY CONCEPTS TEST
Student’s Name:
Tutorial Group:
Teacher’s Name:
Date:
_____________________________________________________________________________________

Motion is a continuous change in position.

Motion at a constant speed in a straight line is called uniform motion.

Position of an object is its location relative to some reference point with 3D coordinates (x, y, and z).
1. How can you tell if an object is undergoing uniform (constant) motion?
[2 marks]

Speed is the distance travelled by an object per unit time.

Distance is the length of path travelled between two points.
2. How can you tell if an object is travelling at constant (uniform) speed?
[2 marks]

Velocity is an object’s displacement (change in position) per unit time.

Displacement is the change in position of an object in a specified direction.
P12: RELATIVITY CONCEPTS TEST  M. J. McGarry (2010)
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3. How can you tell if an object is travelling at constant (uniform) velocity?
[2 marks]
Reference Frames and Relativistic Physics

All motion is measured relative to some frame of reference chosen by the observer. For example,
objects have velocities only with respect to one another. Any statement of an object’s speed must be
made with respect to another object.
Suppose that you are sitting on the backseat of your family’s car, which has just been pulled over by a
police officer because your driver was caught speeding in a 40 km h – 1 school zone. The police officer
says to the driver: “Excuse me, but do you realize that you were driving at 55 km h – 1 in a school zone?”
4. What would be a more physically correct way in which to state the radar-measured speed of the car?
[2 marks]
How does the choice of a frame of reference influence the observation of motion and the motion itself?

The relative velocity in 1 dimension of an object is the velocity with which the object either
approaches or recedes from another object, whether both objects are moving, or only one object is
moving.
5. A child is running in a train, at 3.0 m s – 1, parallel to the length of the train, and towards its front. The
train is travelling down the track at 30.0 m s – 1. What is the child’s velocity relative to the train-track?
[2 marks]
P12: RELATIVITY CONCEPTS TEST  M. J. McGarry (2010)
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Please note: The concept of relative velocity in 2 dimensions is not assessed in this Stage 3 Physics test.

An inertial reference frame is one in which Newton’s First Law is valid: An object continues its
state of rest or motion at constant velocity, unless acted upon by an external unbalanced (or nett or
resultant) force.

Acceleration is the rate of change of an object’s velocity.

An object undergoes constant or uniform acceleration if its velocity changes by equal amounts in
equal time intervals.
Consider that a ball is dropped by a person sitting on a vehicle that is accelerating uniformly to the right.
Information relating to the adjacent sketch diagram:

Ignore the opposing force of air resistance.

Ignore the action force of hands on ball and
the reaction force of ball on hands.

The vehicle is undergoing uniform
(constant) acceleration to the right as shown by the
arrow.
6.
How many additional forces are exerted on
the hand-held ball? Identify and show the forces by
drawing labelled arrows on the sketch.
[2 marks]
7. Is the vehicle an inertial or a non-inertial reference frame? You must explain your answer.
[2 marks]
8. When the ball is dropped, how many forces now act on the falling-ball? Identify and show the forces
by drawing labelled arrows on a redrawn sketch of the falling ball? You must describe your sketch.
P12: RELATIVITY CONCEPTS TEST  M. J. McGarry (2010)
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[2 marks]
What flight-path do you predict for the falling-ball mentioned in Questions 6 through 8?
9. Which flight-path sketch of the ball, shown at equal time intervals, will be observed from the frame of
reference of the ground? You must explain your answer.
[3 marks]
10. Which flight-path sketch of the ball, shown at equal time intervals, will be observed from the frame of
reference of the vehicle? You must explain your answer.
P12: RELATIVITY CONCEPTS TEST  M. J. McGarry (2010)
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[3 marks]
Einstein’s Special Theory of Relativity
Einstein’s special theory of relativity rests on two fundamental assumptions or postulates.
The First Postulate of Special Relativity

First postulate (the relativity principle): The laws of physics have the same form in all uniformly
moving (or inertial) reference frames.

The first postulate of special relativity can be restated as: There is no experiment you can do in an
inertial reference frame to tell if you are at rest or moving uniformly at constant velocity.
The Second Postulate of Special Relativity

Second postulate (constancy of speed of light): Any observer, in any inertial reference frame, will
measure the speed of light travelling through empty space to be exactly c, regardless of the speed of
the light source or that of the observer.
Relativity and Its Consequences
Time Dilation
The time dilation consequence of the theory of relativity can be stated as: Clocks moving relative to an
observer are measured by that observer to run more slowly (as compared to clocks at rest), i.e., moving
clocks are measured to run slow.
Δ t = Δ t O / √ (1 – v 2 / c 2) = γ Δ t O
Where γ = 1 / √ (1 – v 2 / c 2)
c = constant speed of light in free space or vacuum [3.0 × 10 8 m s – 1]
Δ t = time interval of objects (or events) observed as they move by at the speed v
Δ t O = proper time, i.e., time as measured in the rest frame of the objects or events
Length Contraction
Another important consequence of the special theory of relativity is that space intervals – lengths and
distances – are also different in different reference frames. The length contraction consequence of the
special theory of relativity can be stated as: The length of an object is measured to be shorter when it is
moving relative to the observer than when it is at rest.
L = L O × √ (1 – v 2 / c 2) = L O / γ
Where γ = 1 / √ (1 – v 2 / c 2)
c = constant speed of light in free space or vacuum [3.0 × 10 8 m s – 1]
L = length of objects observed as they move by at the speed v
L O = proper length, i.e., length as measured in the rest frame of the objects
P12: RELATIVITY CONCEPTS TEST  M. J. McGarry (2010)
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Relativistic Mass and the Ultimate Speed

The relativistic mass of an object m rel is given by this equation: m rel = m O / √ (1 – v 2 / c 2) = γ m O.
Objects reaching relativistic speeds do not acquire more molecules. In fact, many physicists believe that
an object only has one mass (its rest mass), and that it is only its momentum that increases with speed; a
relativistic effect that everyone agrees with.
An important result of the special theory of relativity is that the speed of an object v cannot equal or
exceed the speed of light c. Do you know why? You will know why after you answer Question 10.
11. What is the relativistic mass m rel of a particle when its speed v = the speed of light c?
[2 marks]
12. How fast would you have to throw a metre ruler to make its length 1/3 of its rest length LO = 1.00 m?
[2 marks]
13. Proxima Centauri, the star nearest to our own, is about 4.2 light years away. (a) If a spaceship could
travel at a speed of 0.80c, what distance, in light years, would a passenger on board the spaceship (as
the reference frame) measure as relativistic distance to Proxima Centauri? [3 marks] (b) How many
Earth years would it take to travel to Proxima Centauri, according to the spaceship’s pilot? [1 mark]
[4 marks]
_____________________________________________________________________________________
P12: RELATIVITY CONCEPTS TEST  M. J. McGarry (2010)
6
[Total marks = 30]
P12: RELATIVITY CONCEPTS TEST  M. J. McGarry (2010)
Percent score =
7