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Introduction of Mechanics Lecture notes 1 Unit of time Measuring time intervals Displacement and distance Displacement in a plane Velocity
Introduction of Mechanics
Lecture notes 1
Unit of time Measuring time intervals Displacement and distance Displacement in a plane Velocity Acceleration
The SI unit of time: second, s
1 Unit of time
No. of...
Definition:1 second is a certain number of vibrations of ‘light wave’ emitted by a cesium atom.
2 Measuring time intervals
Here are some time intervals.
2 Measuring time intervals
Stop-watch is a common instrument for measuring time intervals.
Some stop-watches are accurate to 0.02 s.
Stop-watch and reaction time
Stop-watch and reaction time
average ~ 0.2 s
average ~ 0.2 s
short event
large % error
This time is called reaction time.
Seeing an eventStarting/stopping stop-watch by hand
time
Liu Xiang in the 2004 Olympic Games
Liu Xiang finished 110-m hurdles within 12.91 s in the 2004 Olympic Games.
Discussion:Is it accurate to use the stop-watch to time the race? Why?
Find out some other instruments for time measurement.
Distance = length of path you travelled
l1l2l3
3 Displacement and distance
To go to school from home...your home
your school
= l1 + l2 + l3
your home
your school
A displacement has
Size = length of this arrow
displacement from home to school
displacement from home to school
3 Displacement and distance
To go to school from home...
size& direction.
– Length of a straight line going from the old to the new positions
– Direction of the movement
3 Displacement and distance
Displacement requires :
i.e. size/magnitude
3 Displacement along a straight line
Set an initial point,
Use positive (+) and negative (−) signs to represent the direction.
* Remember assign a direction as positive!
3 Displacement along a straight line
Take the direction to the right as positive.
3 Displacement along a straight line
4 Displacement in a plane
What is the total displacement of the car?
4 Displacement in a plane
From O to A and then to B.From O to A and then to B.
4 km
3 km
37 5 km
total displacement = 3 km to the east
N
a Graphical method
‘tip’ of p joined to ‘tail’ of q
pq
p + q
Tip-to-tail method:
4a Graphical method
5 km
4b Algebraic method
It is easy to add displacements if they are perpendicular to each other.
e.g. N
4 km
3 km
37
52 = 42 + d 2
d = 3 km
5 Velocity
rate of change of displacement.
a speed in a given direction or
velocitya
vector quantit
y
direction
magnitude(speed)
Velocity is...
speed = 300 km h–
1
direction = west
MTR drivers care speed only.
5 Velocity
Pilots care velocity (direction & speed).
speed = 90 km h–
1
Average velocity =overall displacement
total time of travel
direction of velocity = direction of overall displacement
5a Average velocity
The velocity at any instant is called instantaneous velocity.
If a car moves at a constant velocity,
its average and instantaneous velocities are the same.
5b Instantaneous velocity
The direction of velocity along a straight line can be represented by positive (+) and negative (−) signs.
* Remember assign a direction as positive!
5c Velocity along a straight line
5c Velocity along a straight line
e.g. Take direction towards right as positive.
6 AccelerationWhen a car moves faster and faster, its speed is increasing (velocity changed).
When a car moves slower and slower, its speed is decreasing (velocity changed).
When a car changes direction, it accelerates too.
6 Acceleration
Acceleration measures the change in velocity
Acceleration = velocity per unit time
Acceleration = velocity per unit time
direction
speed
overall change in velocitytotal time taken
= m s–2Unit: m s–1/s vector quantity
=
6a Acceleration for motion along a straight line
Like velocity, acceleration can be represented by positive (+) and negative (−) signs.BUT, positive acceleration doesn’t
imply speed-up motion.
6b Acceleration motion with a change in direction
If a car accelerates opposite to its velocity
