Physics
Moments Levers and Gears
Moments, levers, and gears are fundamental concepts in physics that relate to the study of forces and motion. Moments refer to the turning effect of a force, levers are simple machines that amplify force or distance, and gears are mechanical devices that transmit motion and force. Understanding these concepts is crucial for analyzing the behavior of objects and systems in the physical world.
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5 Key excerpts on "Moments Levers and Gears"
eBook - PDF- Nelson Bolívar(Author)
- 2019(Publication Date)
- Arcler Press(Publisher)
Developing means of transforming the motion to accomplish a specific kind required in applications is the main aim of kinematics (Chakrabarti and Bligh, 1996). 2.2. PHYSICAL PRINCIPLES The fundamental physical principles behind the mechanisms are discussed in the following subsections. 2.2.1. Force Force is an influence which when applied on a free body outcome primarily in acceleration and occasionally in elastic deformation of the body. Many kinds of forces are dealt with in our daily life. The earth applies the force of attraction known as a gravitational force for all the bodies on its surface. Pressure is also the force. To analyze these forces acting on bodies, one must have knowledge of how these forces are applied, the direction of force and the value of force. Graphically, forces are symbolized by the vector whose end signifies the point of the action (Subramanian, 1995). 2.2.2. Torque Torque produces or has the tendency to produce the rotation. Its efficiency is calculated by the product of force and the perpendicular distance from the line of the action of the force to the axis of the rotation. Basic Mechanisms in Mechanical Devices 35 The lever shown in Figure 2.1 is a bar which can freely turn about a fixed point A known as the fulcrum . The weight acts on one side of the lever and a balancing force on another side (Sidhu, 2009). Figure 2.1. Lever with the balanced forces. Source: https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt1.html To analyze the levers, torques of forces which are acting on lever need to be found. To obtain torque W about the point A, W must be multiplied by l 1 . In the same way, F x l 2 is torque of force F about the fulcrum A. 2.2.3. Motion Motion is the change of orientation or position. The different kinds of motions are discussed below (Sidhu, 2009; Fogarasy and Smith, 1995). 2.2.3.1. Motion in the Straight Line i. The 1 st step in the study of the motion is to illustrate the position of the moving object.
Available until 9 Apr |Learn more- Carlos A. Smith, Scott W. Campbell(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
239 7 Mechanical Systems: Rotational The focus of Chapter 6 was on systems where the elements moved in pure translation. In this chapter, we will extend the concepts from Chapter 6 to systems where the elements rotate, such as those comprised of gears, wheels, levers, pendulums, or rotating shafts. We will confine ourselves to systems in which each rotating element is a rigid body that is rotating about a single fixed axis. 7.1 Mechanical Law, Moment of Inertia, and Torque Before giving the mechanical law that governs the motion of rotational elements, we have to define displacement, velocity, and acceleration variables that are convenient for describing rotational motion. The symbol θ is used to represent the angular position of an element with respect to a reference position, as shown in Figure 7.1. Angles will be expressed in radians. We define the angular velocity ω as the time rate of change of angular position, ω θ = d dt (7.1) and the angular acceleration α as the time rate of change of angular velocity, α ω θ = = d dt d dt 2 2 (7.2) The positive directions for ω and α will be taken to be the same as that for θ . Note that ω is in rad/s and α is in rad/s 2 . In many applications, these quantities are expressed in terms of degrees or revolutions. If so, they should be converted to radians before using them in calculations. We note that radians are really dimensionless, but we will show “rad” as a unit when it adds clarity to do so, as in the cases of angular position, velocity, and acceleration. In developing free body diagrams (FBDs), we will assume that angular positions and velocities are positive. There are many analogous relations between translational systems and rotational sys-tems. We include several of them in Table 7.1 so that students can more easily make con-nections between the two.
eBook - ePub- Paul Sandori(Author)
- 2016(Publication Date)
- Dover Publications(Publisher)
For 2000 years since Archimedes all writers (including Stevin) belabored this inverse proportionality between forces and lever arms, for the simple reason that the branch of mathematics they were applying was geometry. That was also the only branch of mathematics sufficiently developed at the time. We now convert this ratio into a mathematically equivalent expression, more suited to modern algebra:The product (magnitude of force × lever arm) is called the moment of the force, or torque, and is a measure of its turning effect. The units of moment are those of force and length combined—newton-meters. The lever is balanced on the fulcrum when the moments of the two loads are equal and opposite: the clockwise moment of force B is balanced by the counterclockwise moment of force A. The two moments cancel each other out.Figure 2.10 A beam in equilibrium. The resultant moment of the forces is zero.The concept of moment, thus liberated from the lever where it originated, simplifies many things. For example, is the beam shown in Fig. 2.10 in equilibrium? There is no need to look for a lever to find out. The clockwise moments about the support at point T areThe counterclockwise moment is produced by a force of 24 newtons and is equal to the total clockwise moment:Therefore the beam is in equilibrium. The weight force acting on the beam at its center of gravity was not taken into account because it has no moment about the fulcrum T: the two points coincide and the lever arm of the force is zero.This can be refined further. Moments can turn the body on which they act either in a clockwise or in a counterclockwise sense. We distinguish between the two by giving a positive sign to clockwise moments and a negative sign to those acting in the opposite sense. Then we can add or subtract moments and express the law of the lever in yet another way. The sum total of the moments acting on a body is the resultant moment. The lever is balanced when the resultant moment about the fulcrum is zero. Thus in Fig. 2.10 we haveThe lever is in equilibrium. Suppose we add another 2 newtons to the force acting at point X
eBook - PDFHands-On Science and Technology for Ontario, Grade 4
An Inquiry Approach
- Jennifer Lawson(Author)
- 2020(Publication Date)
- Portage & Main Press(Publisher)
Unit 2 Pulleys and Gears Hands-On Science and Technology for Ontario • Grade 4 s 134 Portage & Main Press, 2018 · Hands-On Science and Technology for Ontario · Hands-On Science and Technology for Ontario, Grade 4 · ISBN: 978-1-55379-939-9 Introduction In this unit of Hands-On Science and Technology for Ontario, Grade 4, students will enhance their understanding of simple machines by looking at two kinds of wheels: pulleys and gears. One or more pulleys are used to move an object from one place to another. Gears can be used in combination to change speed and direction of movement. Students will design and build pulley systems and gear systems, and will explore the advantages of each type of system. By the end of this unit, students will demonstrate an understanding of the characteristics of pulleys and gears, design and make both pulley systems and gear systems, and investigate how motion is transferred from one system to another. They will identify ways in which different systems function and identify appropriate criteria to be considered when designing and making such systems. Students will also have gained a growing familiarity with machines in general. A machine is any device that makes objects move or stops objects from moving. Machines make work easier. To do work, a machine changes the speed, amount, or direction of a force. All machines, no matter how complex, are made up of one or more simple machines. There are six simple machines: the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. Gears are wheel-and-axle mechanisms with teeth that fit together to change the direction of movement. Planning Tips for Teachers ■ Collect references for teacher and student use in advance (see Resources for Students, page 140). Activities and learning centres throughout the unit rely on these resources. ■ The materials needed to complete some activities are extensive.
eBook - ePub- Peter Childs, Peter R. N. Childs(Authors)
- 2018(Publication Date)
- Butterworth-Heinemann(Publisher)
20 Mechanisms Abstract The human race has been inventing and developing mechanisms for as long as our history indicates. The knowledge arising from the operation of these can be leveraged in designing variants, or developments, for modern applications. This chapter serves to introduce a range of mechanisms, some of which will have already been introduced or be familiar, in order to provide an indication of available designs and inspiration for the development of new ones. Keywords Machine; Gizmo; Gadget; Mechanism; Device; Invention; Mechanical Chapter Outline 20.1 Introduction 20.2 Levers 20.3 Pulleys 20.4 Linkages 20.5 Gears, belts and chains 20.6 Rotating and linear motion conversion 20.7 Brakes and clutches 20.8 Time metering 20.9 Miscellaneous devices 20.10 Conclusions References Websites Nomenclature Generally, preferred SI units have been stated. a length (m) c length (m) d pitch diameter (mm) F force (N) F applied applied force (N) F e effort (N) F load load (N) L length (m) m module (mm) M moment (N m) n rotational speed. (rpm) n arm rotational speed of arm (rpm) n sun rotational speed of sun gear (rpm) N number of teeth, number of discs N R number of teeth in ring gear N S number of teeth in sun gear p pressure (N/m 2) r radius (m) R radius (m) T torque (N m) μ coefficient of friction θ angle (rad) ω angular velocity (rad/s) 20.1 Introduction The human race has been inventing and developing mechanisms for as long as our history indicates. The knowledge arising from the operation of these can be leveraged in designing variants, or developments, for modern applications. This chapter serves to introduce a range of mechanisms, some of which will have already been introduced or be familiar, in order to provide an indication of available designs and inspiration for the development of new ones. The term machine element is commonly used for the component parts of a machine which cannot readily be disassembled into simpler components
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