Unbalanced Torque

8 Key excerpts on "Unbalanced Torque"

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  eBook - PDF

  Introduction to Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  The large counterweight on the right side (short end) of this tall tower crane ensures its boom remains balanced on its mast while lifting heavy loads. It is not equal weights on both sides of the tower that keep it in equilibrium, but equal torques. Torque is the rotational analog of force, and is an important topic of this chapter. 9 | Rotational Dynamics Chapter | 9 LEARNING OBJECTIVES After reading this module, you should be able to... 9.1 | Distinguish between torque and force. 9.2 | Analyze rigid objects in equilibrium. 9.3 | Determine the center of gravity of rigid objects. 9.4 | Analyze rotational dynamics using moments of inertia. 9.5 | Apply the relation between rotational work and energy. 9.6 | Solve problems using the conservation of angular momentum. 9.1 | The Action of Forces and Torques on Rigid Objects The mass of most rigid objects, such as a propeller or a wheel, is spread out and not con- centrated at a single point. These objects can move in a number of ways. Figure 9.1a il- lustrates one possibility called translational motion, in which all points on the body travel on parallel paths (not necessarily straight lines). In pure translation there is no rotation of any line in the body. Because translational motion can occur along a curved line, it is often called curvilinear motion or linear motion. Another possibility is rotational motion, which may occur in combination with translational motion, as is the case for the somersaulting gymnast in Figure 9.1b. We have seen many examples of how a net force affects linear motion by causing an object to accelerate. We now need to take into account the possibility that a rigid object can also have an angular acceleration. A net external force causes linear motion to change, but what causes rotational motion to change? For example, something causes the rotational velocity of a speedboat’s propeller to change when the boat accelerates.

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  Introductory Physics for the Life Sciences: Mechanics (Volume One)

  • David V. Guerra(Author)
  • 2023(Publication Date)
  • CRC Press

    (Publisher)

  3 Torque and Rotational Equilibrium

  DOI: 10.1201/9781003308065-3

  3.1 Introduction

  In some situations, a force is applied using a tool like a wrench or a screwdriver and a twisting force, called a torque, is produced. These twisting forces are central to the understanding and analysis of some objects in equilibrium. In this chapter, the concepts of torque will be studied and then applied to the analysis of systems in rotational equilibrium.

  • Chapter question: A person suspends a block of mass m from his or her hand, as depicted in Figure 3.1 .
    FIGURE 3.1 Diagram of an arm.
    Assuming their forearm has a mass mA , is the force of tension in their bicep muscle equal to, greater than, or less than the sum of the weight of their arm and the weight of the object? To answer this question, the concepts of torque and rotational equilibrium will be developed and they will be applied at the end of this chapter to answer this question.

  3.2 Torque

  Torque is a twisting force, which is denoted by the Greek letter tau (τ). When opening the lid of a jar, the more force you apply the more twisting force (torque) you apply to open the jar. As you may also know from experience, if you are trying to loosen or tighten a bolt with a wrench, the harder you pull on the wrench, the force (F), the more torque there is on the bolt. But sometimes the bolt will not loosen no matter how hard you pull on the wrench. To loosen the bolt you can get a longer wrench or even slip a pipe on the end of the wrench. So, it is clear that the torque depends not only on the force applied but also on the distance away from the rotation point at which the force is applied.

  In the previous example, the angle between the force and the distance away from the rotation point is assumed to be perpendicular as shown in Figure 3.2 , but that is not always the case. So, the torque (τ) is defined as the product of the applied force (F) and the perpendicular distance (

  r ⊥

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  LEARNING OBJECTIVES After reading this module, you should be able to... 9.1 Distinguish between torque and force. 9.2 Analyze rigid objects in equilibrium. 9.3 Determine the center of gravity of rigid objects. 9.4 Analyze rotational dynamics using moments of inertia. 9.5 Apply the relation between rotational work and energy. 9.6 Solve problems using the conservation of angular momentum. Mr. Green/Shutterstock CHAPTER 9 Rotational Dynamics The large counterweight on the right side (short end) of this tall tower crane ensures its boom remains balanced on its mast while lifting heavy loads. It is not equal weights on both sides of the tower that keep it in equilibrium, but equal torques. Torque is the rotational analog of force, and is an important topic of this chapter. 9.1 The Action of Forces and Torques on Rigid Objects The mass of most rigid objects, such as a propeller or a wheel, is spread out and not concentrated at a single point. These objects can move in a number of ways. Figure 9.1a illustrates one possibility called translational motion, in which all points on the body travel on parallel paths (not necessarily straight lines). In pure translation there is no 223 Translation ( ) a Combined translation and rotation ( ) b FIGURE 9.1 Examples of (a) translational motion and (b) combined translational and rotational motions. 224 CHAPTER 9 Rotational Dynamics rotation of any line in the body. Because translational motion can occur along a curved line, it is often called curvilinear motion or linear motion. Another possibility is rotational motion, which may occur in combination with translational motion, as is the case for the somersaulting gymnast in Figure 9.1b. We have seen many examples of how a net force affects linear motion by causing an object to accelerate. We now need to take into account the possibility that a rigid object can also have an angular acceleration.

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  Cutnell & Johnson Physics, P-eBK

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  CHAPTER 9 Rotational dynamics LEARNING OBJECTIVES After reading this module, you should be able to: 9.1 distinguish between torque and force 9.2 analyse rigid objects in equilibrium 9.3 determine the centre of gravity of rigid objects 9.4 analyse rotational dynamics using moments of inertia 9.5 apply the relation between rotational work and energy 9.6 solve problems using the conservation of angular momentum. INTRODUCTION The large counterweight on the right side (short end) of this tall tower crane ensures its boom remains balanced on its mast while lifting heavy loads. It is not equal weights on both sides of the tower that keep it in equilibrium, but equal torques. Torque is the rotational analog of force, and is an important topic of this chapter. Source: Mr. Green / Shutterstock 9.1 The action of forces and torques on rigid objects LEARNING OBJECTIVE 9.1 Distinguish between torque and force. The mass of most rigid objects, such as a propeller or a wheel, is spread out and not concentrated at a single point. These objects can move in a number of ways. Figure 9.1a illustrates one possibility called translational motion, in which all points on the body travel on parallel paths (not necessarily straight lines). In pure translation there is no rotation of any line in the body. Because translational motion can occur along a curved line, it is often called curvilinear motion or linear motion. Another possibility is rotational motion, which may occur in combination with translational motion, as is the case for the somersaulting gymnast in figure 9.1b. FIGURE 9.1 Examples of (a) translational motion and (b) combined translational and rotational motions Translation ( ) a Combined translation and rotation ( ) b We have seen many examples of how a net force affects linear motion by causing an object to accelerate. We now need to take into account the possibility that a rigid object can also have an angular acceleration.

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  Biomechanics For Dummies

  • Steve McCaw(Author)
  • 2014(Publication Date)
  • For Dummies

    (Publisher)

  V .

  A New Angle on Newton: Angular Versions of Newton's Laws

  Newton's laws of motion (see Chapter 6 ) explain that an unbalanced force causes an acceleration of a body, meaning the magnitude of the acceleration is proportional to the magnitude and direction of the unbalanced force and inversely proportional to the body's mass, and that forces equal in magnitude and opposite in direction are applied to the two bodies interacting to produce the force. In most human motion, the mass of the body stays constant, and only the motion of the body can change.

  Torque (see Chapter 8 ) is the turning effect of a force. If an applied force does not pass through a specified axis of rotation, the force has a moment arm around the axis and creates a torque on the body. When more than one torque acts around an axis, calculating the net torque at the axis (ΣT axis ) shows if an Unbalanced Torque (ΣT axis ≠ 0; see Chapter 8 for more on calculating net torque) is present around the axis. Newton's laws of motion explain the effect of an Unbalanced Torque on the angular motion of a body.

  The two main points to remember in looking at Newton's laws for angular motion are that the moment of inertia — the resistance to changing angular motion — is not necessarily constant for a body, and a force must have a moment arm to produce a turning effect on a body. In the following sections, I explain Newton's laws of angular motion.

  Maintaining angular momentum: Newton's first law

  Newton's first law, also known as the law of conservation of angular momentum, specifies that an unbalanced external torque causes a change in the angular momentum of a body. Angular momentum is the product of the moment of inertia (I ) and the angular velocity (ω), or H = I

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  Practical Balancing of Rotating Machinery

  • Derek Norfield(Author)
  • 2011(Publication Date)
  • Elsevier Science

    (Publisher)

  This means that for a given speed there is a con-stant inward acceleration. This in turn means that a centripetal (inward) force is acting on the unbalance. We now need the third law to complete the relationship. Newton’s third law The third law states that every action causes an equal and opposite reaction. This is the key to understanding what we are doing by balancing a rotor. If an object is moving along a curved path the direction of its velocity is changing, and therefore a force is acting on it. Energy balance 67 The force responsible for this change in direction is, as dis-cussed above, called the centripetal force. It is directed toward the center of curvature. By definition the unbalance is attached to a rotor. The centripetal force is reacted by an equal outward force which we are very familiar with. Centrifugal (outward) force is the reaction of the rotor/bearing system to the rotating unbalance. If we are referencing the unbalance the force is inward – centripetal. If we are referencing the rotor then we are refer-encing the outward – centrifugal force. The unbalance causes a force on the bearings or a vibration of the rotor. When we balance a rotor we are compensating the unbalance mass to reduce the force and vibration. Energy balance There is always a balance of energy input and energy output. It is easy to see the result of a single action, or a simple sequence of actions. Baseball The Pitcher throws the ball (imparts energy to it). The Hitter swings the bat (putting energy into that). The Bat hits the ball. The energy in the ball is reflected and most of the bat’s energy is added to that of the ball resulting in it moving in a new direction with a new (higher) speed and energy level while the bat has a lower energy level. Golf Another example is the golfer. He swings the driver giving it a huge amount of kinetic energy.

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  BIOS Instant Notes in Sport and Exercise Biomechanics

  • Paul Grimshaw, Neil Fowler, Adrian Lees, Adrian Burden(Authors)
  • 2007(Publication Date)
  • Routledge

    (Publisher)

  Section C – Kinetics of angular motion

  C1	TORQUE AND THE MOMENT OF FORCE

  Key Notes

  Torque	A torque is a twisting or turning moment that is calculated by multiplying the force applied by the perpendicular distance (from the axis of rotation) at which the force acts (the moment arm). Torques cause angular accelerations that result in rotational movement of limbs/segments.
  Clockwise and anti-clockwise rotation	Clockwise rotation is the rotary movement of a limb/lever/segment in a clockwise direction (−ve). Clockwise is referring, in this case, to the hands of a clock or watch. Anti-clockwise rotation is rotary movement in the opposite direction (+ve).
  Force couple	A force couple is a pair of equal and opposite parallel forces acting on a system.
  Equilibrium	This is a situation in which all the forces and moments acting are balanced, and which results in no rotational acceleration (i.e., a constant velocity situation).
  Second condition of equilibrium	This states that the sum of all the torques acting on an object is zero and the object does not change its rotational velocity. Re-written, this condition can be expressed as the sum of the anti-clockwise and clockwise moments acting on a system is equal to zero (∑ACWM + ∑CWM = 0).
  Application	Swimmers are now utilizing a pronounced bent elbow underwater pull pattern during the freestyle arm action. This recent technique change allows the swimmer to acquire more propulsive force and yet prevent excessive torques being applied to the shoulder joint (which were previously caused by a long arm pull underwater pattern). Large torques are needed at the hip joint (hip extensor and flexor muscles) to create the acceleration of the limbs needed to kick a soccer ball.

  Torque

  A torque is defined as a twisting or turning moment. The term moment is the force acting at a distance from an axis of rotation. Torque can therefore be calculated by multiplying the force applied by the perpendicular distance at which the force acts from the axis of rotation. Often the term torque is referred to as the moment of force. The moment of force is the tendency of a force to cause rotation about an axis. Torque is a vector quantity and as such it is expressed with both magnitude and direction. Within human movement or exercise science torques cause angular acceleration that result in the rotational movements of the limbs and segments

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  Predicting Motion

  • Robert Lambourne(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  2 , acting in opposite directions along the rotation axis. We said earlier that when balance was achieved the two torques would have the same magnitude, which is true, but you can now see that due to their opposed directions, the vector sum of the two torques would actually have been zero. Hence the lack of any net turning effect.

  Figure 4.17 The vector sum of balanced torques about the rotation axis is zero, Γ 1 + Γ 2 = 0.

  A general point to be drawn from this discussion is the following:

  When several different torques act at a point, the total torque at that point is given by the vector sum of the individual torques.

  Note that torques are vectors, so they must be added like vectors.

  Question 4.3 Given the orientations of r 1 F 1 , r 2 and F 2 in Figure 4.17 , describe how you would confirm that Γ 1 and Γ 2 have the correct orientations? Have they, in fact, been drawn with the correct orientations?

  Question 4.4 A rectangular sheet of metal, with sides of length 0.400 m and 0.300 m, rests on a horizontal surface and is pivoted at one corner (point O in Figure 4.18 ) so that it can rotate about the z-axis. Two horizontal forces F 1 , and F 2 of the same magnitude, 5 N, are applied simultaneously at the points indicated in Figure 4.18 . Work out the total torque at O due to these forces and hence determine the direction in which the metal sheet will rotate. ■

  Figure 4.18 Which way will the object turn? See Question 4.4.

  2.4 Torque and angular motion

  Broadly speaking, as you saw in Chapter 1 , forces cause translational acceleration. In similarly broad terms, it is also true that torques cause angular acceleration.

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