FORCE AND NEWTON’S LAWS
1. Ancient view: objects tend to stop if they are in motion; force is required to keep
something moving. This was a natural thing to believe in because we see objects
stop moving after some time; frictionless motion is possible to see only in rather
special circumstances.
2. Modern view: objects tend to remain in their initial state; force is required to
change motion. Resistance to changes in motion is called inertia. More inertia
means it is harder to make a body accelerate or decelerate.
3. Newton’s First Law: An object will remain at rest or move with constant velocity
unless acted upon by a net external force. (A non-accelerating reference frame is
called an inertial frame; Newton’s First Law holds only in inertial frames.)
4. More force leads to more acceleration:
5. The greater the mass of a body, the harder it is to change its state of motion. More
mass means more inertia. In other words, more mass le
⇒ ∝a F
ads to less acceleration:
1
Combine both the above observations to conclude that:
6. Newton's Second Law: (or, if you pref
a
m
F
a
m
F
a
m
⇒ ∝
∝
= er, write as ).
7. is one relation between three independent quantities ( , , ). For it to be
useful, we must have separate ways of measuring mass, acceleration, and force.
Accelerati
F ma
F ma m a F
=
=
on is measured from observing the rate of change of velocity; mass is a
measure of the amount of matter in a body (e.g. two identical cars have twice
the mass of a single one). Forces (due to g
-2
ravity, a stretched spring, repulsion of
two like charges, etc) will be discussed later.
8. Force has dimensions of [mass] [acceleration] . In the MKS system
the unit of force is the
× = M LT
2
Newton. It has the symbol N where:
1 Newton = 1 kilogram.metre/second .
9. Forces can be internal or external. For example the mutual attraction of atoms
within a block of wood are called internal forces. Something pushing the wood is an external force. In the application of , remember that stands for the
total external force upon the body.
10. Forces are vectors, and so they must be added vectorially:
F ma F =
123
This means that the components in the ˆ direction must be added separately, those in
the direction separately, etc. ˆ
11. Gravity acts directly on the
FFF F
x
y
= + + +⋅⋅⋅⋅
rrr r
1 11 2
mass of a body - this is a very important experimental
observation due to Newton and does not follow from . So a body of mass
experiences a force while a body of mass exper
F ma
m F mg m
=
=
2 2
iences a force
, where is the acceleration with which any body (big or small) falls under
the influence of gravity. (Galileo had established this important fact when he dropped
F mg g =
different masses from the famous leaning tower of Pisa!)
12. The weight of a body is the force which gravity exerts upon it, . Mass and
weight are two completely different quantities. So, f
W W mg =
or example, if you used a spring
balance to weigh a kilo of grapes on earth, the same grapes would weigh only 1/7 kilo
on the moon.
13. Newton's Third Law: for every action there is an equal and opposite reaction. More
precisely, , where is the force exerted by body upon whereas
is the force exerted by body upon . Ask yourself what would happen if this wa
FF F B A F AB BA AB BA
A B
= −
s not
true. In that case, a system of two bodies, even if it is completely isolated from the
surroundings, would have a net force acting upon it because the net force acting upon
both bodies would be 0.
14. If action and reaction are always equal, then why does a body accelerate at all? Students
are often confused by this. The answer: in considering the acceleration o
F F AB BA + ≠
f a body you must
consider only the (net) force acting upon that body. So, for example, the earth pulls a stone
towards it and causes it to accelerate because there is a net force acting upon the stone. On
the other hand, by the Third Law, the stone also pulls the earth towards it and this causes the
earth to accelerate towards the stone. However, because the mass of the earth is so large, we
are only able to see the acceleration of the stone and not that of the earth.
1. Ancient view: objects tend to stop if they are in motion; force is required to keep
something moving. This was a natural thing to believe in because we see objects
stop moving after some time; frictionless motion is possible to see only in rather
special circumstances.
2. Modern view: objects tend to remain in their initial state; force is required to
change motion. Resistance to changes in motion is called inertia. More inertia
means it is harder to make a body accelerate or decelerate.
3. Newton’s First Law: An object will remain at rest or move with constant velocity
unless acted upon by a net external force. (A non-accelerating reference frame is
called an inertial frame; Newton’s First Law holds only in inertial frames.)
4. More force leads to more acceleration:
5. The greater the mass of a body, the harder it is to change its state of motion. More
mass means more inertia. In other words, more mass le
⇒ ∝a F
ads to less acceleration:
1
Combine both the above observations to conclude that:
6. Newton's Second Law: (or, if you pref
a
m
F
a
m
F
a
m
⇒ ∝
∝
= er, write as ).
7. is one relation between three independent quantities ( , , ). For it to be
useful, we must have separate ways of measuring mass, acceleration, and force.
Accelerati
F ma
F ma m a F
=
=
on is measured from observing the rate of change of velocity; mass is a
measure of the amount of matter in a body (e.g. two identical cars have twice
the mass of a single one). Forces (due to g
-2
ravity, a stretched spring, repulsion of
two like charges, etc) will be discussed later.
8. Force has dimensions of [mass] [acceleration] . In the MKS system
the unit of force is the
× = M LT
2
Newton. It has the symbol N where:
1 Newton = 1 kilogram.metre/second .
9. Forces can be internal or external. For example the mutual attraction of atoms
within a block of wood are called internal forces. Something pushing the wood is an external force. In the application of , remember that stands for the
total external force upon the body.
10. Forces are vectors, and so they must be added vectorially:
F ma F =
123
This means that the components in the ˆ direction must be added separately, those in
the direction separately, etc. ˆ
11. Gravity acts directly on the
FFF F
x
y
= + + +⋅⋅⋅⋅
rrr r
1 11 2
mass of a body - this is a very important experimental
observation due to Newton and does not follow from . So a body of mass
experiences a force while a body of mass exper
F ma
m F mg m
=
=
2 2
iences a force
, where is the acceleration with which any body (big or small) falls under
the influence of gravity. (Galileo had established this important fact when he dropped
F mg g =
different masses from the famous leaning tower of Pisa!)
12. The weight of a body is the force which gravity exerts upon it, . Mass and
weight are two completely different quantities. So, f
W W mg =
or example, if you used a spring
balance to weigh a kilo of grapes on earth, the same grapes would weigh only 1/7 kilo
on the moon.
13. Newton's Third Law: for every action there is an equal and opposite reaction. More
precisely, , where is the force exerted by body upon whereas
is the force exerted by body upon . Ask yourself what would happen if this wa
FF F B A F AB BA AB BA
A B
= −
s not
true. In that case, a system of two bodies, even if it is completely isolated from the
surroundings, would have a net force acting upon it because the net force acting upon
both bodies would be 0.
14. If action and reaction are always equal, then why does a body accelerate at all? Students
are often confused by this. The answer: in considering the acceleration o
F F AB BA + ≠
f a body you must
consider only the (net) force acting upon that body. So, for example, the earth pulls a stone
towards it and causes it to accelerate because there is a net force acting upon the stone. On
the other hand, by the Third Law, the stone also pulls the earth towards it and this causes the
earth to accelerate towards the stone. However, because the mass of the earth is so large, we
are only able to see the acceleration of the stone and not that of the earth.
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