the relation between force and motion id described in Newtons three laws of motion. These laws are very simple statements and enable us to describe the future (or past) motion of body if we know the forces acting on it.
the relation between force and motion id described in Newtons three laws of motion. These laws are very simple statements and enable us to describe the future (or past) motion of body if we know the forces acting on it.
Newton's First Law of Motion: I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. This we recognize as essentially Galileo's concept of inertia, and this is often termed simply the "Law of Inertia".
This PPT covers projectile motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructors as well as students.
Describes displacement, velocity, acceleration as vectors and distance and speed as scalars, Show all needed equations and their use.
**More good stuff available at:
www.wsautter.com
and
http://www.youtube.com/results?search_query=wnsautter&aq=f
Newton's First Law of Motion: I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. This we recognize as essentially Galileo's concept of inertia, and this is often termed simply the "Law of Inertia".
This PPT covers projectile motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructors as well as students.
Describes displacement, velocity, acceleration as vectors and distance and speed as scalars, Show all needed equations and their use.
**More good stuff available at:
www.wsautter.com
and
http://www.youtube.com/results?search_query=wnsautter&aq=f
Rotational dynamics as per class 12 Maharashtra State Board syllabusRutticka Kedare
This ppt is as per class 12 Maharashtra State Board's new syllabus w.e.f. 2020. Images are taken from Google public sources and Maharashtra state board textbook of physics. Gif(videos) from Giphy.com. Only intention behind uploading these ppts is to help state board's class 12 students understand physics concepts.
Week 3 OverviewLast week, we covered multiple forces acting on.docxmelbruce90096
Week 3 Overview
Last week, we covered multiple forces acting on an object. This week we will cover motion in two dimensions, inclined planes, circular motion, and rotation.
Forces in Two Dimensions (1 of 2)
So far you have dealt with single forces acting on a body or more than two forces that act parallel to each other. But in real life situations more than one force may act on a body. How are Newton's laws applied to such cases? We will restrict the forces to two dimensions.
Since force and acceleration are vectors, Newton's law can be applied independently to the X and Y-axes of a coordinate system. For a given problem you can choose a suitable coordinate system. But once a coordinate system is chosen, we have to stick with it for that problem. The example that follows shows how to find the acceleration of a body when two forces act on it at right angles to each other.
Forces in Two Dimensions (2 of 2)
To find the resultant acceleration we draw an arrow OA of length 3 units along the X-axis and then an arrow AB of length 4 units along the Y-axis. The resultant acceleration is the arrow OB with the length of 5 units. Therefore, the acceleration is 5 m/s2 in the direction of OB. Also when you measure the angle AOB with a protractor, we find it to be 53°.
The acceleration caused by the two forces is 5 m/s2 at an angle of 53°.
Uniform Circular Motion
When an object travels in a circular path at a constant speed, its motion is referred to as uniform circular motion, and the object is accelerated towards the center of the circle. If the radius of the circular path is r, the magnitude of this acceleration is ac = v2 / r, where v is its speed and ac is called the centripetal acceleration. A centripetal force is responsible for the centripetal acceleration, which constantly pulls the object towards the center of the circular path. There cannot be any circular motion without a centripetal force.
Banking
When there is a sharp turn in the road or when a turn has to be taken at a high speed as in a racetrack, the outer part of the road or the track is raised from the inner part of the track. This is called banking. It provides additional centripetal force to a turning vehicle so that it doesn't skid.
The angle of banking is kept just right so that it provides all the centripetal force required and a motorist does not have to depend on the friction force at all.
Inclined Planes
Forces on an Inclined Plane
The inclined plane is a device that reduces the force needed to lift objects. Consider the forces acting on a block on an inclined surface. The inclined surface exerts a normal force FN on the block that is perpendicular to the incline. The force of gravity, FG, points downward. If there is no friction, the net force, Fnet, acting on the block is the resultant of FN and FG. By Newton's second law the net force must point down the incline because the block moves only along the incline and not perpendicular to it.
The vector triangle shows .
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. Linear Motion
All objects considered previously have
been point objects. This makes it easy to
do calculations but inaccurate.
A point object has no dimensions,
therefore it can’t rotate. All objects
rotate to some extent.
3. Axis of Rotation
A body will rotate about an axis.
The axis can internal as in a CD or external as in a
boomerang.
5. Bodies
A body can be rigid or non-rigid, that is the body
may have moving parts.
Consider,
Paint being stirred.
A rubiks cube.
A diver.
6. Circular Motion
An object moving in a circular path will
have a constant speed.
It is continually changing direction,
therefore it’s velocity is continually
changing.
A relationship can be determined for the
speed of the object.
To do this some terms must be defined first.
7. Circular Motion Terms
Period
Is the time needed to complete one
cycle/rev (in secs). The symbol T is used.
Frequency
Number of cycles/revs completed per unit
time.
Units are Hertz (Hz)
T
1
f =
8. Circular Motion Terms
In uniform circular motion, the object in one
revolution moves 2πr in T seconds.
T
rv π2=
t
sv=
9. Try Example 1
The Earth has a diameter of 1.276 x 107
m.
Find the average linear speed of a point
on the Earth’s equator.
10. Solution
r = 1.276 x 107
/2 = 6.38 x 106
m
T = 24 x 60 x 60 = 8.64 x 104
s
v = 464 ms-1
(over 1600 km h-1
)
T
rv π2=
4
6
10x8.64
10x6.38xx2 π=v
11. Centripetal Acceleration
A particle undergoing
uniform circular motion is
continually changing
velocity.
∴ acceleration is
changing.
v
v
v
a
b
c
- va
∆v1
12. Centripetal Acceleration
∆v1
= vb
- va.
∆v2
= vc
- vb
and so on.
The magnitude of ∆v1
= ∆v2.
The direction is always to
the centre of the circle.
v
v
v
a
b
c
- va
∆v1
13. Centripetal Acceleration
The acceleration which produces these
velocity changes in a direction…..
is called centripetal (centre seeking)
acceleration.
The direction is always towards the centre
of the circular motion.
15. Average Acceleration
Defined as:
where ∆v = vf
- vi
.
The instantaneous acceleration a at
any instant can be obtained by allowing
the time interval to become infinitesimal.
t∆
∆= va
_
16. Direction of Acceleration
Stone attached to a string and whirled above the
head. What type of motion has it?
Circular.
If string breaks, what happens?
Stone flies off in a direction that is tangential to the
point at which the string breaks.
At any point, the tangent to the point gives the
direction of the velocity.
17. Relationship Between a and v
in Circular Motion
The magnitude of this acceleration is constant for a given
speed and radius.
Circular Motion
Newton’s 2nd
law tells us that a centripetal acceleration can only
happen if there is an unbalanced force.
r
c
2
va =
18. Force Causing the Centripetal
Acceleration
Any particle undergoing uniform circular motion is
acted upon by an unbalanced force which is….
Constant in magnitude.
Directed towards the centre of the circle.
Causes the Centripetal Acceleration.
19. Force Causing the Centripetal
Acceleration
When an object undergoes uniform circular
motion there is a net force which is directed
towards the centre of the circle,
The force has a physical origin
Gravity
Normal Force
Tension
Friction
21. Force Causing the Centripetal
Acceleration
With a centripetal force, the object moves in a circular
path.
22. Force Causing the Centripetal
Acceleration
When the unbalanced force is released:
the object moves along a tangential path,
at a constant velocity.
23. Gravity
Moon revolving around the
Earth:
Directed towards the centre
of the Earth,
Holds the moon in a near
circular orbit.
25. Friction
Car rounding a corner:
Sideways frictional force,
Directed towards centre of turn,
Force between car tyre and road.
If force not great enough:
Car skids.
26. Tension
Billy can being swung.
Vertically or horizontally
The tension force between
arm and can
causes the can to move in
circular motion.
27. Force Causing the Centripetal
Acceleration
The force can be found by
combining Newton’s 2nd
Law and
the equation for centripetal
acceleration.
r
m c
2
and vaaF ==
r
m
2
vF =
28. Example
◦ r = 1m
◦ F = 196 N
◦ m = 1 kg
Determine v
r
mm
2
vaF ==
29. Solution – Part (a)
v = 14 ms-1
tangential to the circle at the
point of release.
1
1x196=v
m
rFv=
30. Repeat for a vertical circle
◦ F = 196 N
◦ m = 1 kg
◦ r = 1 m
◦ g = 9.8 ms-2
◦ v = ?
31. Solution – Part (b)
Maximum tension occurs
at the bottom of the
path.
Tension must be sufficient
both to provide the
centripetal force and……
balance the gravitational
force.
32. Solution – Part (b)
gvF m
r
m +=
2
+= 9.8x1
1
x1196
2
v
v2
=196 - 9.8 = 186.2
v =13.6 ms-1
33. Angular displacement
Objects moving in circular motion go through angular
displacements (θ). A quarter circle has an angular
displacement of 90 degrees, a full circle has 360
degrees, from P to Q in the diagram it is 60 degrees.
The arc length is the distance traced
on the circle – this is a different displace-
ment to the straight line between P and Q.
True angular displacements are the angles measured
in radians (not degrees)
35. Angular and linear speed
Angular speed is
ω = θ/t
with units of rads/s
And this can be related to linear speed
of arc length/ time
V = r θ /t
then
V = r ω
36. Angular velocity
Velocity is speed with a direction so for angular
velocity we need to determine the direction.
This is found using the right hand rule. Your right hand
in a fist form, with the fingers curling in the direction of
the objects rotation. Your thumb then gives the
angular velocity direction. This is always
perpendicular to the plane of rotation
38. Centripetal Acceleration and
Friction
When a car turns a corner,you feel as though
you are pushed against the side of the car,
away from the direction that the car is
turning.
What is actually happening is:
You are trying to move in a straight line while the
car is moving in a circular path. The back of the
seat (friction) or the door of the car exerts a force
on you.
40. Centripetal Acceleration and
Friction
The car itself must also have a force acting on it to
turn around the bend.
If the road is flat, the force is the friction between
the tires and the road.
41. Centripetal Acceleration and
Friction
Under some conditions:
water or ice on the road
excessive speed
Frictional force is not enough.
Car will skid in a near straight line path.
Cars & Ice
Cars and Ice 2
42. Centripetal Acceleration and the
Normal Force
A car turns on a banked section of curved
road:
the chances of skidding is reduced.
44. Centripetal Acceleration and
the Normal Force
What does this mean?
Not only does friction supply the force to turn the
car, so does some of the normal force.
Can the entire force be supplied by horizontal
component of normal force?
Yes; at one specific angle
This angle is given by:
45. Centripetal Acceleration and
the Normal Force
In the vertical direction, there are 2 forces;
FN
cos θ acting upwards and mg acting
downwards.
As there is no net vertical motion:
FN
cos θ = mg
Now dividing by
r
v
mFN
2
sin =θ
46. Centripetal Acceleration and
the Normal Force
For any radius curve and ideal speed, the
perfect banking angle can be found.
rg
v2
tan =θ
mg
r
v
m
F
F
N
N
2
cos
sin
=
θ
θ
47. Questions
Find the angular speed of the rotation of the
Earth?
Find the angular velocity of a vinyl record spinning
at 30 rpm?
Find the banking angle for a 35m radius turn at
60kph?
