MECHANICS
What is a scalar quantity?
A scalar quantity is a quantity which only has magnitude and has no direction, for
example speed
What is a vector quantity?
A vector quantity is a quantity which has both magnitude and a direction, for
example velocity
Sometimes, why are scalar and vector quantities used interchangeably?
Although scalar and vector quantities are two different types of quantities with
completely different meanings, in cases of one-directional motion, the values of
scalar and vector quantities are always equal. So there is no difference between
them in this case.
What is speed?
Speed is the rate of change distance
What is distance?
Distance is the total length travelled by an object between two positions
What is velocity?
Velocity is the rate of change of displacement in a specific direction
Why can velocity be talked about in terms of speed?
Because velocity is just speed in a specific direction (Vector quantity)
What is displacement?
It is the shortest distance travelled by an object from its initial position to its final
position
What is average speed?
Average speed is the speed of a whole journey, which is found by dividing the total
distance by the total time to cover that distance
What is average velocity?
MECHANICS 1
, Average velocity is the velocity of a whole journey which is found by dividing the
total displacement by the total time taken for that displacement to take place
What is instantaneous speed?
It is the speed of an object at a particular instant in time
What is instantaneous velocity?
It is the velocity of an object at a particular instant in time
What is acceleration?
It is the rate of change of velocity in a specific direction
What does the slope of a d-t graph represent?
It represents the speed
What does the slope of a s-t graph represent?
It gives the velocity
What does the area under a velocity/speed-time graph represent?
Displacement/Distance
What does the area under an acceleratiom time graph give?
Change in velocity
What does a straight line mean on a velocity-time graph?
It means the acceleration is constant
What does a straight line mean on a distance/displacement-time graph?
It means the distance/displacement is constant, so the object is at rest
What does the area under a force-time graph give?
It gives the change in momentum (impulse)
What does the area under a change of momentum against time graph give?
It gives the resultant force
What does the slope of a momentum against time graph give?
The acceleration
MECHANICS 2
, What is resultant force?
The total force acting on an object by adding up all the forces acting on it, taking
into account their directions, using vector addition
What is a free-body force diagram?
It is a diagram where an object is shown isolated, and all the forces acting on it are
drawn in using arrows from the points where they act
What are the different methods of adding two vectors?
Triangle law method, Parallelogram law method, and scaled drawing method
What is the cosine and sine rule?
How to use parallelogram method for adding two vectors?
What is centre of mass?
It is the point within the object that moves as if the entire mass of the object is
present at that point
What is centre of gravity?
It is the point within the object through which the entire weight of the object seems
to act
Is centre of mass and centre of gravity the same?
We generally consider g to be constant and so they are in the the same location,
and thus they are the same.
MECHANICS 3
, Why centre of mass and centre of gravity are not the same if there is a significant
change in g?
If there is a change in g, then the parts of the object which are closer to the center
of the earth will experience a stronger gravitational field strength. Thus, they will be
more strongly attracted by Earth’s gravity than the parts farther away. So the centre
of gravity will be nearer to the region which is experiencing a greater force of
attraction by the Earth’s gravity instead of being in the same location as the centre
of mass, as this does not depend on g
Why is the centre of gravity important?
Because it can affect the motion of objects. If the object is applied through the
centre of gravity, it will produce only linear acceleration. However, if the force is not
applied through the centre of gravity, then the force will still produce the same
magnitude of linear acceleration (assuming the force is constant), but it will also
produce a moment/torque on the object.
Where is the centre of gravity of regular, uniform density objects?
At the centre
Where is the centre of gravity of irregular/non-uniform density objects?
This has to be determined experimentally, however we can predict that the centre of
gravity will be in the more dense region for non-uniform density objects
How does the centre of gravity of objects shift when their shape changes?
How does the stability of objects work?
When objects topple over, or are tilted to one side, they rotate around a pivot. Thus,
we can use moments in this situation to describe its motion around the pivot. If the
centre of gravity is present above the base of the object, the object will not topple
over. However, if the centre of gravity does not lie above the base, then the object
will topple over as at that point, there will be a net moment which causes the object
to topple. You can also consider the pivot point instead of the entire base
Diagram of stability of objects
MECHANICS 4
, MECHANICS 5
What is a scalar quantity?
A scalar quantity is a quantity which only has magnitude and has no direction, for
example speed
What is a vector quantity?
A vector quantity is a quantity which has both magnitude and a direction, for
example velocity
Sometimes, why are scalar and vector quantities used interchangeably?
Although scalar and vector quantities are two different types of quantities with
completely different meanings, in cases of one-directional motion, the values of
scalar and vector quantities are always equal. So there is no difference between
them in this case.
What is speed?
Speed is the rate of change distance
What is distance?
Distance is the total length travelled by an object between two positions
What is velocity?
Velocity is the rate of change of displacement in a specific direction
Why can velocity be talked about in terms of speed?
Because velocity is just speed in a specific direction (Vector quantity)
What is displacement?
It is the shortest distance travelled by an object from its initial position to its final
position
What is average speed?
Average speed is the speed of a whole journey, which is found by dividing the total
distance by the total time to cover that distance
What is average velocity?
MECHANICS 1
, Average velocity is the velocity of a whole journey which is found by dividing the
total displacement by the total time taken for that displacement to take place
What is instantaneous speed?
It is the speed of an object at a particular instant in time
What is instantaneous velocity?
It is the velocity of an object at a particular instant in time
What is acceleration?
It is the rate of change of velocity in a specific direction
What does the slope of a d-t graph represent?
It represents the speed
What does the slope of a s-t graph represent?
It gives the velocity
What does the area under a velocity/speed-time graph represent?
Displacement/Distance
What does the area under an acceleratiom time graph give?
Change in velocity
What does a straight line mean on a velocity-time graph?
It means the acceleration is constant
What does a straight line mean on a distance/displacement-time graph?
It means the distance/displacement is constant, so the object is at rest
What does the area under a force-time graph give?
It gives the change in momentum (impulse)
What does the area under a change of momentum against time graph give?
It gives the resultant force
What does the slope of a momentum against time graph give?
The acceleration
MECHANICS 2
, What is resultant force?
The total force acting on an object by adding up all the forces acting on it, taking
into account their directions, using vector addition
What is a free-body force diagram?
It is a diagram where an object is shown isolated, and all the forces acting on it are
drawn in using arrows from the points where they act
What are the different methods of adding two vectors?
Triangle law method, Parallelogram law method, and scaled drawing method
What is the cosine and sine rule?
How to use parallelogram method for adding two vectors?
What is centre of mass?
It is the point within the object that moves as if the entire mass of the object is
present at that point
What is centre of gravity?
It is the point within the object through which the entire weight of the object seems
to act
Is centre of mass and centre of gravity the same?
We generally consider g to be constant and so they are in the the same location,
and thus they are the same.
MECHANICS 3
, Why centre of mass and centre of gravity are not the same if there is a significant
change in g?
If there is a change in g, then the parts of the object which are closer to the center
of the earth will experience a stronger gravitational field strength. Thus, they will be
more strongly attracted by Earth’s gravity than the parts farther away. So the centre
of gravity will be nearer to the region which is experiencing a greater force of
attraction by the Earth’s gravity instead of being in the same location as the centre
of mass, as this does not depend on g
Why is the centre of gravity important?
Because it can affect the motion of objects. If the object is applied through the
centre of gravity, it will produce only linear acceleration. However, if the force is not
applied through the centre of gravity, then the force will still produce the same
magnitude of linear acceleration (assuming the force is constant), but it will also
produce a moment/torque on the object.
Where is the centre of gravity of regular, uniform density objects?
At the centre
Where is the centre of gravity of irregular/non-uniform density objects?
This has to be determined experimentally, however we can predict that the centre of
gravity will be in the more dense region for non-uniform density objects
How does the centre of gravity of objects shift when their shape changes?
How does the stability of objects work?
When objects topple over, or are tilted to one side, they rotate around a pivot. Thus,
we can use moments in this situation to describe its motion around the pivot. If the
centre of gravity is present above the base of the object, the object will not topple
over. However, if the centre of gravity does not lie above the base, then the object
will topple over as at that point, there will be a net moment which causes the object
to topple. You can also consider the pivot point instead of the entire base
Diagram of stability of objects
MECHANICS 4
, MECHANICS 5
