Physics
Rotational Motion
Rotational motion refers to the movement of an object around an axis. It involves the rotation of an object, such as a wheel or a spinning top, and is characterized by angular displacement, velocity, and acceleration. This type of motion is governed by principles such as torque, angular momentum, and moment of inertia.
Written by Perlego with AI-assistance
Related key terms
1 of 5
7 Key excerpts on "Rotational Motion"
eBook - PDF- Richard L. Myers(Author)
- 2005(Publication Date)
- Greenwood(Publisher)
Q Rotational Motion Introduction In translational motion, an object moves from one point to another. Another type of motion occurs when an object moves in a curved path. This type of motion is called Rotational Motion. Examples of rota- tional motion are all around us. A spinning compact disc, the wheels of a car, and a blowing fan are a few common examples of Rotational Motion. As you sit reading this book, you are in constant Rotational Motion as the Earth spins on its axis. Rota- tional motion may accompany translational motion, as when a ball rolls down a ramp. It may also occur in the absence of trans- lational motion, as when a top spins on its axis. Rotation refers to the circular move- ment of an object about an axis that passes through the object. Another type of curved motion occurs when an object moves about an axis outside of it. This is called a revo- lution. Both rotational and revolutionary motion will be considered in this chapter, and the term Rotational Motion will be used as a generic description for curved motion. Many of the concepts for Rotational Motion parallel those for translational motion. The simplest type of Rotational Motion is uni- form circular motion. Uniform Circular Motion Circular is used as a general term to describe motion along a curved path and should not be interpreted to mean motion following a perfect circle; for instance, elliptical motion is classified as circular motion. Common examples of circular motion include the orbital motion of sat- ellites, amusement park rides, rounding a curve in a car, and twirling an object on the end of a string. Many of the concepts describing translational motion have anal- ogous counterparts for circular motion. These will be developed in this chapter. The concepts in this chapter apply to both rota- tional and revolutionary motion. Rotation involves circular motion around an axis that passes through the object itself, for example, a rotating top.
eBook - PDF- John Matolyak, Ajawad Haija(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
139 © 2010 Taylor & Francis Group, LLC Rotational Motion Translational motion and circular motion, uniform and nonuniform of an object, were discussed in Chapters 3 and 4. In this chapter, Rotational Motion of a point or extended object will be introduced. A force acting on an extended object creates a torque that rotates it about a fixed axis. A solid object of finite physical size is known as a rigid body. The axis of rotation could be about the center of mass of the rigid body or about other points where it is pivoted. In this chapter, Sections 8.2 through 8.7 discuss the kinematics of a rigid body, and Section 8.8 reviews the dynamics of the rigid body. In addition to drawing a parallel between Newton’s laws applied to point-like objects in linear motions and those applied to Rotational Motion of a rigid body, translational and Rotational Motions of a rigid body are discussed in detail. 8.1 ANGULAR KINEMATIC QUANTITIES Consider a point-like object moving in a circle of radius r (Figure 8.1). As the object moves from point P 1 at t 1 to point P 2 at t 2 , it sweeps through an arc Δ s that subtends an angle Δθ ( = θ 2 – θ 1 ) at the center, in a time interval Δ t = t 2 – t 1 . From geometry Δ s = r Δθ , (8.1) where Δθ is an angular displacement, measured in radians. To convert an angle expressed in degrees to radians, the following relation may be used: θ π θ rad deg deg 2 rad 360 = , (8.2a) and from radians to degrees, the conversion is θ π θ de g r ad 360 2 . = (8.2b) Dividing Equation 8.1 by Δ t gives the average linear velocity v ; that is, ∆ ∆ ∆ ∆ s t r t = θ or v r . = ω (8.3) For an object experiencing a constant linear acceleration, v v v 2 1 2 = + . 8 140 Essential Physics © 2010 Taylor & Francis Group, LLC Here, v 1 and v 2 are the instantaneous tangential, or linear, velocities of the object at points P 1 and P 2 , respectively.
eBook - PDFWorkshop Physics Activity Guide Module 2
Mechanics II
- Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Name Section Date UNIT 12: Rotational Motion Siegfried Haasch/Getty images Electricity is generated when the wind causes these large turbines to spin around in Rotational Motion. As can be observed by the blurring in the photograph, each point on the turbine moves at a different speed, with those farther from the rotation axis moving at faster speeds. But even though these points are all moving at different speeds, there is obviously something similar about their motion. In particular, each point on the turbine travels in a complete circle each time the wheel makes one full rotation. In this unit, we will learn how to describe such motion and how to approach solving problems that involve rotations. 390 WORKSHOP PHYSICS ACTIVITY GUIDE UNIT 12: Rotational Motion OBJECTIVES 1. To understand the concepts of rotational position, velocity, and accelera- tion, as well as the associated kinematic equations. 2. To develop a definition for rotational inertia as a measure of the resistance to changes in Rotational Motion. 3. To understand torque and its relation to rotational acceleration and rota- tional inertia. 12.1 OVERVIEW We have studied the characteristics of an object undergoing translational motion, usually along a straight line, but also for objects traveling in circular motion or projectile motion. By “translational” motion we mean the motion of the object’s center of mass (or equivalently, the motion of a point mass), ignoring any rotation of the object. But in the real world, many objects will also rotate as they move. A rolling wheel, Earth spinning on its axis, and a hammer that tumbles when tossed are a few examples. However, our current formulation of Newton’s second law only applies to the center-of-mass (translational) motion of an object. In this unit we will define several new quantities and relationships to describe the Rotational Motion of rigid objects, objects that do not change their shape as they move.
eBook - PDF- Stephen McKnight, Christos Zahopoulos(Authors)
- 2015(Publication Date)
- Cambridge University Press(Publisher)
3 Rotational Motion While we have been discussing Newton’s Laws so far, mass – resistance to acceleration – has been considered as a scalar quantity. No matter which direction you apply a force to a point object, its mass is the same. This simple formalism breaks down when we consider Rotational Motion. If we have a long cylinder, it matters very much whether we rotate it about an axis down the center of the cylinder or an axis which is perpendicular to the cylinder! This will require us to extend the concept of resistance to acceleration to depend on the direction of the rotation. 3.1 Rotational Motion and moment of inertia Consider a mass attached to a string rotating in a circle one complete rotation each second, as shown in Figure 3.1. The speed, the magnitude of the velocity, is constant. Geometry gives us that the arc length s is related to the radius and the angle that the arc transects by s ¼ θr where θ is the angle in radians as shown in Figure 3.2. (Note if θ is 2π radians – 360 degrees – this gives us arc length ¼ circumference ¼ 2πr, and we recover our familiar relation that circumference ¼ π diameter.) The speed is the time derivative of the distance traveled (the arc length): |v| ¼ ds/dt ¼ r dθ/dt ¼ rω where ω ¼ dθ/dt is the angular velocity in radians per second. At each moment, the ball has a velocity which is tangential to the circle. Since the direction of the velocity is constantly changing – even if the speed is constant – the ball is undergoing constant acceleration. This centripetal acceleration is caused by the force exerted on the string to pull the ball into a circular path. As illustrated in Figure 3.3, when the angle changes by a small dθ, the change in velocity d v ! is directed toward the center of the circle.
eBook - PDF- Stephen Lee(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
Dynamics of rigid bodies rotating about a fixed axis The human mind has first to construct forms, independently, before we can find them in things. Einstein, 1879–1955 20.1 A rigid body rotating about a fixed axis You might not be able to answer all these questions fully now, but the issues involved should become clearer as you work through this chapter. It is reasonable to treat a large object as a particle when every part of it is moving in the same direction with the same speed, but clearly this is not always the case. The particles in a rotating wheel have different velocities and accelerations and are subject to different forces. The laws of particle dynamics which you have used so far need to be developed so that they can be applied to the rotation of large objects. 20 Q UESTION 20.1 So far you have modelled moving objects as particles. In many circumstances this is reasonable, but how would you model the motion of the sails of a windmill or the other objects illustrated in the pictures above? Do the two children on the roundabout have the same kinetic energy? What is the kinetic energy of a rotating wheel? Definitions You are already familiar with many aspects of rotation such as the angular speed and acceleration of a particle and you have also taken moments to determine the turning effect of a force, but it is as well to be clear about what is meant by some of the terms involved before continuing with the discussion. Rigid bodies Wheels can be modelled as rigid bodies. A rigid body is such that each point within it is always the same distance from any other point. You are not a rigid body but a hard chair is one (molecular vibrations being ignored). The axis of rotation When you lean back on your chair, it might rotate about a point, say A, at the end of one leg. You will have more control, however, if it rotates about the axis formed by the line joining the ends, A and B, of two legs.
eBook - PDF- 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.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
That is, the cylinder would go faster at the bottom. Chapter 10 | Rotational Motion and Angular Momentum 365 Check Your Understanding Analogy of Rotational and Translational Kinetic Energy Is rotational kinetic energy completely analogous to translational kinetic energy? What, if any, are their differences? Give an example of each type of kinetic energy. Solution Yes, rotational and translational kinetic energy are exact analogs. They both are the energy of motion involved with the coordinated (non-random) movement of mass relative to some reference frame. The only difference between rotational and translational kinetic energy is that translational is straight line motion while rotational is not. An example of both kinetic and translational kinetic energy is found in a bike tire while being ridden down a bike path. The Rotational Motion of the tire means it has rotational kinetic energy while the movement of the bike along the path means the tire also has translational kinetic energy. If you were to lift the front wheel of the bike and spin it while the bike is stationary, then the wheel would have only rotational kinetic energy relative to the Earth. PhET Explorations: My Solar System Build your own system of heavenly bodies and watch the gravitational ballet. With this orbit simulator, you can set initial positions, velocities, and masses of 2, 3, or 4 bodies, and then see them orbit each other. Figure 10.20 My Solar System (http://cnx.org/content/m42180/1.8/my-solar-system_en.jar) 10.5 Angular Momentum and Its Conservation Why does Earth keep on spinning? What started it spinning to begin with? And how does an ice skater manage to spin faster and faster simply by pulling her arms in? Why does she not have to exert a torque to spin faster? Questions like these have answers based in angular momentum, the rotational analog to linear momentum. By now the pattern is clear—every rotational phenomenon has a direct translational analog.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
