Here are the key points about centripetal force: - It is a force that pulls an object towards the center of its circular path. - It continuously changes the direction of motion but not the speed. - The centripetal force formula relates this force to mass, speed, and radius of the circular motion. - Examples include forces that keep planets in orbit or cause objects to travel in circular loops like a roller coaster.

1. Newton's Second Law

2. Forces are Unbalanced
There is an acceleration
The acceleration depends The acceleration depends
Directly upon the inversely upon the
〝 net force 〞 〝 object mass 〞

3. Newton's Second Law
• The acceleration of an object as produced by a net
force is directly proportional to the magnitude of the
net force, in the same direction as the net force, and
inversely proportional to the mass of the object.
This verbal statement can be expressed in equation
form as follows:
a = Fnet / m
The net force is equated to the product of the mass
times the acceleration.
Fnet = m × a

4. • The acceleration of an object increases with
increased force, decreases with increased
mass, and is in the same direction as the force.

7. Sampe Problem
• What force is needed to accelerate a 10kg shopping
cart 3 m/s2?
• If a 5 kg ball is accelerating 1.2 m/s2, what is the force
on it ?
• A person on a scooter is accelerating 2 m/s2. If the
person has a mass of 50 kg, how much force is acting
on that person?

8. Sampe Problem
• If a team pulls with a combined force of 9000N on an
airplane with a mass of 30000 kg, What is the
acceleration of the airplane?
• Half the people on the team decide not to pull the
airplane. The combined force of those left is 4500N,
While the airplane’s mass is still 30000 kg. What will
be the acceleration?
• A girl pulls a wheeled backpack with a force of 3N.
If the backpack has a mass of 6 kg. What is its
acceleration?

9. Sampe Problem
• A model rocket is accelerating at 2 m/s2. The force on
it is 1N. What is the mass of the rocket?
• Another model rocket is accelerating at a rate of 3
m/s2 with a force of 1N. What is the mass of the
rocket?
• A boy pushes a shopping cart with a force of 10N,
and the cart accelerates 1 m/s2. What is the mass of
the cart?

10. 【 Example 】
1. Determine the accelerations that result when a
12-N net force is applied to a 3-kg object and
then to a 6-kg object.
A 3-kg object experiences an acceleration of 4 m/s2.
A 6-kg object experiences an acceleration of 2 m/s2.

11. 【 Example 】
2. A net force of 15 N is exerted on an encyclopedia to
cause it to accelerate at a rate of 5 m/s2. Determine the
mass of the encyclopedia.
Use Fnet= m * a with Fnet = 15 N and a = 5 m/s2.
So (15 N) = (m)*(5 m/s2)
And m = 3.0 kg

12. 【 Example 】
3. Suppose that a sled is accelerating at a rate of 2 m/s2.
If the net force is tripled and the mass is doubled,
then what is the new acceleration of the sled?
Answer: 3 m/s2
The original value of 2 m/s/s must be multiplied by 3
(since a and F are directly proportional) and divided
by 2 (since a and m are inversely proportional)

13. 【 Example 】
• An applied force of 50 N is used to accelerate an
object to the right across a frictional surface. The
object encounters 10 N of friction. Use the diagram to
determine the normal force, the net force, the mass,
and the acceleration of the object. (Neglect air
resistance.)

14. Newton's third law

15. Forces act in pairs.
1. Newton's third law relates action and reaction
forces.
The key points to Newton“s third law are that when
objects A and B interact ，
the force of A on B equals the force of B on A; and
the forces are opposite in direction.
In action/reaction pairs either force can be
considered the action force or the reaction
force.The two forces occur simultaneously ．

16. • Example ： When you push down on a table ， the
force from the table's resistance increases instantly to
match your force.
Action/reaction force pairs occur when any two
objects interact, not just through contact forces.
• Example ： The pull of Earth on a falling baseball is
exactly that of the baseball on Earth.Earth is so much
more massive,however,that Earth's acceleration from
the pull is nearly nothing.The acceleration of the
baseball is quite noticeable ．

17. 2.Newton's three laws describe and
predict motion
• Newton‘s laws work together to explain changes in
the motion of objects,such as a squid moving forward
when squirting water backward,or a bird flying higher
or changing direction.
• Newton's laws are also useful in calculating how
objects move under the conditions found in everyday
life.Scientists such as Albert Einstein have added to
our understanding of motion since Newton's
time.Under certain conditions, such as extreme speed
or extreme gravity,Newton's laws need to be adjusted.

18. Newton's Third Law
• For every action, there is an equal and
opposite reaction.
The statement means that in every interaction, there is a
pair of forces acting on the two interacting objects. The
size of the forces on the first object equals the size of the
force on the second object. The direction of the force on
the first object is opposite to the direction of the force
on the second object. Forces always come in pairs - equal
and opposite action-reaction force pairs.

19. Consider the flying motion of
birds.
• A bird flies by use of its wings.
• The wings of a bird push air downwards.
Since forces result from mutual interactions,
the air must also be pushing the bird upwards.

20. • ：地球對書本的
吸引力 ,
• ：書本對地球的
吸引力。
• 且為作用力與
反作用力。

21. 1. Who was the scientist who gave us the Laws of
Motion?
2. How many Laws of Motion are there?
3. What is another name for the first law of motion?
4. Which law explains why we need to wear seatbelts?
5. Which law says that force is equal to mass times
acceleration (F=MA)?
6. Which law says that heavier objects require more
force than lighter objects to move or accelerate them?
7. Which law explains how rockets are launched into
space?
8. Which law says that for every action there is an equal
and opposite reaction?

22. • 1. Who was the scientist who gave us the Laws
of Motion?
• Answer: Sir Isaac Newton
2. How many Laws of Motion are there?
• Answer: three
3. What is another name for the first law of
motion?
• Answer: Law of Inertia
4. Which law explains why we need to wear seat
belts?
• Answer: First Law of Motion

23. 5. Which law says that force is equal to mass
times acceleration (F=MA)?
• Answer: Second Law of Motion
6. Which law says that heavier objects require
more force than lighter objects to move or
accelerate them?
• Answer: Second Law of Motion
7. Which law explains how rockets are launched
into space?
• Answer: Third Law of Motion
8. Which law says that for every action there is
an equal and opposite reaction?
• Answer: Third Law of Motion

24. Forces can change the direction of
motion.
• Force can change the direction of an object
without changing its speed if the force acts at
right angles to the motion.
• A force that continuously acts at right angles to
an object's motion will pull the object into
circular motion.
• Any force that keeps an object moving in a
circle at a constant speed is called a centripetal
force.

25. • The centripetal force needed to keep an object
moving in a circle depends on the mass of the
object, the speed of the object,and the radius
of the circle.
• Centripetal force =
mass‧ speed 2
radius