Torque is a rotational force that depends on three main factors: the distance from the axis of rotation (lever arm), the angle of the applied force, and the magnitude of the applied force. Torque causes an object to rotate and is measured in Newton-meters. Systems in rotational equilibrium have no net torque, meaning the sum of all torques acting on the object is zero. This allows seesaws and diving boards to remain balanced. Solving rotational equilibrium problems involves drawing free body diagrams and setting the sum of torques equal to zero.
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
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
this is about center of mass, center of mass for complicated shapes, center of mass of hemisphere, center of mass of many particles, center of mass of solids, center of mass of uniform cylinder, center of mass of uniform rod
This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
this is about center of mass, center of mass for complicated shapes, center of mass of hemisphere, center of mass of many particles, center of mass of solids, center of mass of uniform cylinder, center of mass of uniform rod
This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
Physics 161Static Equilibrium and Rotational Balance Intro.docxrandymartin91030
Physics 161
Static Equilibrium and Rotational Balance
Introduction
In Part I of this lab, you will observe static equilibrium for a meter stick suspended horizontally. In Part II, you will observe the rotational balance of a cylinder on an incline. You will vary the mass hanging from the side of the cylinder for different angles.
Reference
Young and Freedman, University Physics, 12th Edition: Chapter 11, section 3
Theory
Part I: When forces act on an extended body, rotations about axes on the body can result as well as translational motion from unbalanced forces. Static equilibrium occurs when the net force and the net torque are both equal to zero. We will examine a special case where forces are only acting in the vertical direction and can therefore be summed simply without breaking them into components:
(1)
Torques may be calculated about the axis of your choosing:
(2)
where torque is specified by the equation:
(3)
where d is the lever arm (or moment arm) for the force. The lever arm is the perpendicular distance from the line of force to the axis about which you are calculating the torque.
Normally, up is "+" and down is "-" for forces. For torques, it is convenient to define clockwise as "-" and counterclockwise as "+". Whatever you decide to do, be consistent with your signs and make sure you understand what a "+" or "-" value for your force or torque means directionally.
Part II: Any round object when placed on an incline has tendency of rotating towards the bottom of an incline. If the downward force that causes the object to accelerate down the slope is canceled by another force, the object will remain stationary on the incline. Figure 1 shows the configuration of the setup. In order to have the rubber cylinder in static equilibrium we should satisfy the following conditions:
(4)
Figure 1: Experimental setup for Part II
The condition that the net force along the x-axis (which is conveniently taken along the incline) must be zero yields the relationship. (Prove this!)
Without static friction the cylinder would slide down the incline; the presence of friction causes a torque in clockwise (negative) direction. In order to have static equilibrium we need to balance that torque with a torque in counterclockwise direction. This is achieved by hanging the appropriate mass m.
Applying the last condition to the center of the cylinder will result in:
where r, the radius of the small cylinder (PVC fitting), is the moment arm for the mass m and R, the radius of the rubber cylinder, is the moment arm for the frictional force which accounts for M and m. Combining this equation with the equation for Ffr from above will result in:
(5)
(6)
By adjusting the mass m, we can observe how the equilibrium can be achieved.
Procedure
Part I: Static Equilibrium
Figure 2: Diagram of Torque Experiment Setup
1. Weigh the meter stick you use, including the metal hangers.
2. Attach .
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
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.
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!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2. What is Torque?
Torque is a rotational force around a fixed
axis or point.
3. Torque
Torque is represented using the Greek letter
tau as follows:
τ = Fd sinθ
-Where
F = Force (Newtons)
d = lever arm length
θ = angle that force makes with the
axis of the lever arm
Note: Torque is a vector quantity.
4. Factors that affect Torque
Distance: The distance from the point of rotation affects
torque in such a manner that the further you are from the
axis of rotation, the easier it is to rotate around that point.
F1
F2
d2
d1
Note: The distance d is also known as the lever arm.
5. Factors that affect Torque
Angle: Torque also depends on the angle at which the
force makes with the lever arm. Torque is maximum
when the force makes a 90° angle with the lever arm.
d
F
θ
θ
6. Factors that affect Torque
Force: Torque is directly proportional to the force
applied to the lever arm. As the force increases, so
does the torque.
F1
d
F2
d
F2 > F1
τ2 > τ1
7. Torque & Seesaws
Equilibrium: Equilibrium exits when the seesaw is
balanced such that it will not tend to rotate around
the fulcrum.
– At Equilibrium:
There is no net torque
There is no net force.
Fulcrum
8. Conditions for Equilibrium
1. The sum of the forces must equal zero.
– ΣF = F1 + F2 – FF = 0
– ΣF = m1g + m2g – FF = 0
1. The sum of the torques must equal zero.
– Στ = F1d1 + F2d2 = 0
9. Translational Equilibrium
The sum of the forces must equal zero.
– ΣF = F1 + F2 – FF = 0
– ΣF = m1g + m2g – FF = 0
F1 F2
FF
10. Rotational Equilibrium
The sum of the torques must equal zero.
– Στ = F1d1 + F2d2 = 0
– Note that one torque will provide a rotational force in
the counterclockwise direction (F1) while the other
force will provide a rotational force in the clockwise
direction (F2)
F1 F2
d1 d2
11. Center of Mass
If the fulcrum (pivot point) does not occur at
the center of the object, then the center of
mass must be factored into the problem.
For uniform geometric shapes, the center of
mass can be conveniently chosen at the
center of the object.
Center of Mass
12. When the Fulcrum is not in the Center
Στ = F1d1 + F2d2 + FB1dB1 + FB2dB2 = 0
F1
F2
Center of mass of
board relative to the
fulcrum.
FB1
FB2
d1
dB1 dB2
d2
13. Solving Problems involving Torque
1. Select the object to which the equations for equilibrium are to
be applied.
2. Draw a free-body diagram that shows all of the external
forces acting on the object.
3. Choose a convenient set of x, y axes and resolve all forces
into components that lie along these axes.
4. Apply the equations that specify the balance of forces at
equilibrium. (Set the net force in the x and y directions equal
to zero.)
5. Select a convenient axis of rotation. Set the sum of the
torques about this axis equal to zero.
6. Solve the equations for the desired unknown quantities.
14. A woman whose weight is 530 N is
poised at the right end of a diving board
with length 3.90 m. The board has
negligible weight and is supported by
a fulcrum 1.40 m away from the left
end.
Find the forces that the bolt and the
fulcrum exert on the board.
Example 1: A Diving
Board
15. 022 =−=∑ WWF τ
( )( ) N1480
m1.40
m90.3N530
2 ==F
2
2
WW
F =
Example 1: A Diving
Board
17. Torque Applied to Mobiles
The mobile can be looked at as a balance of
forces in motion.
The forces of nature – wind and gravity –
play a significant role in understanding how
mobiles function.
