2. Dynamics
Mass
; quantitative measure of an object's
resistance to the change of its motion.
***In this chapter, we consider that and
object has a uniform mass.
Force
; any influence that causes an object to
undergo a certain change, either
concerning its movement, direction, or
geometrical construction.
Newton’s Laws of motion
Newton’s 1st law
“Every object of constant mass will
continue in its state of rest or uniform
velocity in a straight line unless an
external resultant force acts on it to
change its state.”
Newton’s 2nd law
“When a resultant force acts on an
object of constant mass, the object will
accelerate and move in the direction of
the resultant force. The product of the
mass and acceleration of the object is
equal to the resultant force.”
Newton’s 3rd law
“For every action, there is an equal and
opposite reaction, and these forces act
on mutually opposite bodies.”
𝐹 = 0
𝐹 = 𝑚𝑎
***Normal force is not a reaction force
for 𝑚𝑔, the reaction force for 𝑚𝑔 is the
force that the object attract the Earth!!!
Newton's law of universal
gravitation
Kepler's laws of planetary motion
Kepler’s 1st law – Orbital law
“The orbit of every planet is an ellipse
with the Sun at one of the two foci.
(singular; focus)”
Kepler’s 2nd law – Law of Area
“A line joining a planet and the Sun
sweeps out equal areas during equal
intervals of time.”
𝐴1 = 𝐴2
𝐹 = 𝐺
𝑚1 𝑚2
𝑟2
𝑆𝑢𝑛
𝑃𝑙𝑎𝑛𝑒𝑡
𝑆𝑢𝑛
𝑡
𝑡
𝐴1
𝐴2
𝑃1
𝑃2
𝑃3
𝑃4
3. 𝑇2
∝ 𝑅3
Kepler’s 3rd law – Law of Period
“The square of the orbital period of a
planet is directly proportional to the
cube of the semi-major axis of its orbit.”
Momentum
2 types;
Translational(linear) momentum
Angular momentum
Translational momentum, 𝒑
𝐹 = 𝑚𝑎
𝐹 = 𝑚
𝑑𝑣
𝑑𝑡
𝐹 =
𝑑𝑚𝑣
𝑑𝑡
𝐹 =
𝑑𝑝
𝑑𝑡
Angular momentum, 𝑳
𝐿 = 𝑟𝑝
𝐿 = 𝑟𝑚𝑣
𝐿 = 𝑟𝑚𝜔𝑟
𝐿 = 𝑚𝑟2
𝜔
𝐿 = 𝐼𝜔
𝑝 = 𝑚𝑣
𝐹 =
𝑑𝑝
𝑑𝑡
𝑝 − 𝑝0 = ∆𝑝 = 𝐹(𝑡)
𝑡
𝑡0
𝑑𝑡
𝐹
𝑡
𝑖𝑚𝑝𝑢𝑙𝑠𝑒
Impulse
; an impulse ,𝐼 is defined as the integral
of a force with respect to time.
***an area under 𝐹-𝑡 graph is the
impulse
Conservation of linear momentum
𝑝𝑖 = 𝑝 𝑓
***no external force acts on the system
Collisions
Elastic collision – the total 𝐾𝐸 and 𝑝 are
conserved
𝑝 𝑓 = 𝑝𝑖
𝐾𝐸𝑓 = 𝐾𝐸𝑖
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑎𝑝𝑝𝑟𝑜𝑎𝑐ℎ
= 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑖𝑜𝑛𝐿 = 𝐼𝜔
𝑢1 − 𝑢2 = 𝑣2 − 𝑣1
