Newton’s Laws of Motion

by

Izzul Syahmi Bin Che Russlee

PPISMP Sains

Newton’s First Law of Motion

Newton’s First Law

“Every body persists in its state of being at rest or of moving uniformly straight

forward, except insofar as it is compelled to change its state by force

impressed.”

Sir Isaac Newton

Newton’s First Law

Newton’s First Law

• Newton's first law is also called the law of inertia. It states that if the vector sum of all forces (that is, the net force) acting on an object is zero, then the acceleration of the object is zero and its velocity is constant.

Newton’s First Law

• The first point needs no comment, but the second seems to violate everyday experience. For example:

For example, a hockey puck sliding along ice does not move forever; rather, it slows and eventually comes to a stop.

Newton’s First Law

• According to Newton's first law, the puck comes to a stop because of a net external force applied in the direction opposite to its motion.

• This net external force is due to a frictional force between the puck and the ice, as well as a frictional force between the puck and the air.

• If the ice were frictionless and the puck were travelling in a vacuum, the net external force on the puck would be zero and it would travel with constant velocity so long as its path were unobstructed.

Newton’s First Law

Newton’s First Law

Newton’s Second Law of Motion

Newton’s Second Law

“The change of momentum of a body is proportional to the impulse impressed

on the body, and happens along the straight line on which that impulse is

impressed.”

Sir Isaac Newton

Newton’s First Law

Newton’s Second Law

• Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading:

If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

Newton’s Second Law

• Using modern symbolic notation Newton's second law can be written as a vector differential equation:

F = Force Vector

m = Mass of the body

v = Velocity Vector

t = Time

Newton’s Second Law

• Because the mass m is constant, it can be moved outside the differential operator:

• Then, by substituting the definition of acceleration, this differential equation can be rewritten in the form:

Newton’ Second Law

• The product of the mass and velocity is momentum p (which Newton himself called "quantity of motion"). Therefore, this equation expresses the physical relationship between force and momentum.

• Consistent with the law of inertia, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude. The equation implies that, under zero net force, the momentum of a body is constant.

Newton’s Second Law

• Thus the acceleration of an object is proportional to the force applied to it, and inversely proportional to the object's mass.

• Newton's second law requires modification if the effects of special relativity are to be taken into account, since it is no longer true that momentum is the product of inertial mass and velocity.

Newton’s Second Law

• Example

• Two forces act on an object of mass 2.0kg which is placed on a smooth horizontal plane. Determine the acceleration of the object.

2kg

a

45º 30º

10 N6 N

Newton’s Second Law

• Answer– Since the object slides on the horizontal

direction, we can find the net external force F acting on the object in this direction

F = 10 cos 30º- 6 cos 45º = 4.4 NF = ma4.4 = 2a

a = 2.2 ms , to the right -2

Newton’s Third Law of Motion

Newton’s Third Law

“To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always

equal and are directed in opposite directions”

Sir Isaac Newton

Newton’s Third Law

Newton’s Third Law

Newton’s Third Law

• During the interaction, F X on Y acts on Y while at the same time F Y on X acts on X. Hence, action and reaction must act on different body.

Newton’s Third Law

• Example

• Two objects, masses m1=50kg and m2=150kg, are tied to a light string and at rest on a smooth horizontal floor, as shown.

m2 m1 P

Newton’s Third Law

• Determine– The horizontal force P acting on the object so

that the acceleration of objects is 4.0 ms -2

m1

a

T P

Newton’s Third Law

– AnswerP-T = m a

The object is pulling tension in the string

T = m a

P = (m + m )a

=(50-150)(4) = 800 N

1

1

1 2

1 2

(2)

(1)

Newton’s Third Law

• Determine the tension in the string connecting the two object

• Answer • Substitute P = 800N into (2)

T = (150)(4) = 600N

a

m2 T

The End

Thank You