Angular Kinematics

3 Key excerpts on "Angular Kinematics"

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  eBook - ePub

  Biomechanics For Dummies

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

    (Publisher)

  angular acceleration refers to speeding up or slowing down the angular velocity of a body. Use the sign of the acceleration and the direction of the motion to interpret a calculated acceleration.

  Relating Angular Motion to Linear Motion

  To throw a ball, coordinated angular motions of body segments are used to increase the speed of the hand holding the ball. At release, the ball becomes a projectile, and its path through the air is described using linear kinematics (see Chapter 5 ). The relationship between angular motion and linear motion explains how rotations increase linear velocity and lead to success in all throwing and kicking activities (baseball, softball, soccer) and in activities when an implement (club, stick, or bat) is swung to strike a target object (golf ball, puck, or baseball). This section explains the relationships between linear and Angular Kinematics, beginning with displacement, moving on to velocity, and ending with acceleration.

  This section links measures of Angular Kinematics and linear kinematics. Chapter 5 explains linear speed, linear velocity, and linear acceleration in more detail and also covers the topic of projectile motion.

  Angular displacement and linear displacement

  The definition of rotation is that all points on the rotating body undergo the same angular displacement. But points on the rotating body travel different linear distances during the same period of rotation, depending on how far a point is from the axis of rotation. The axis of rotation is the identified line around which a body rotates. The axis of rotation for a gymnast swinging on the high bar is easily identified because the hands grip the bar. However, in other swinging movements, there is often no clearly observable axis, and the axis must be specified and used for the analysis.

  Figure 9-6

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  eBook - ePub

  Higher Engineering Science

  • William Bolton(Author)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  4 Linear and angular motion 4.1 Introduction This chapter is concerned with the behaviour of dynamic mechanical systems when there is uniform acceleration. The terms and basic equations associated with linear motion with uniform acceleration and angular motion with uniform angular acceleration, Newton’s laws of motion, moment of inertia and the effects of friction are revised and applied to the solution of mechanical system problems. The terms scalar quantity and vector quantity are used in this chapter, so as a point of revision: Scalar quantities are those that only need to have their size to be given in order for their effects to be determined, e.g. mass. Vector quantities are those that need to have both their size and direction to be given in order for their effects to be determined, e.g. force where we need to know the direction as well as the size to determine its effect. 4.2 Linear motion The following are basic terms used in the description of linear motion, i.e. motion that occurs in a straight line path rather than rotation which we will consider later in this chapter: 1 Distance and displacement The term distance tends to be used for distances measured along the path of an object, whatever form the path takes; the term displacement, however, tends to be used for the distance travelled in a particular straight line direction (Figure 4.1). For example, if an object moves in a circular path the distance travelled is the circumference of the path whereas the displacement might be zero if it ends up at the same point it started from

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  eBook - ePub

  Doing Physics with Scientific Notebook

  A Problem Solving Approach

  • Joseph Gallant(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  Rotational Kinematics

  Not all rotational motion is uniform; in non-uniform circular motion, the angular speed changes. The average angular acceleration is the rate of change of the angular speed

  (7.7)

  where Δω = ω - ω0 is the change in angular speed. The usual unit for angular acceleration is the rad/s2 , but we’ll also use rev/min2 .

  From the definitions of angular displacement, speed, and acceleration, we can derive four basic equations which describe the angular position and speed of objects rotating with a constant acceleration.

  (7.8a)

  (7.8b)

  (7.8c)

  (7.8d)

  For constant angular acceleration, the average angular speed is .

  Do these equations look familiar? These are the same as Eqs. (2.5) from Chapter 2. The connection between these angular quantities and their linear counterparts is the radius R of the circular path.

  The radius is perpendicular to the displacement, velocity, and the component of the acceleration that changes the object’s speed.

  Example 7.5

  Turn that crap off

  After the LP record in our first two examples is finished, you turn it off and it slows to a stop after 10 seconds. Calculate the record’s angular acceleration, assuming it to be constant. How many times does the record turn while it is slowing down?

  Solution.

  Since we want Δθ in revolutions, let’s use Eq. (7.7) to Evaluate the acceleration in revolutions and minutes.

  Now that we know the time and angular acceleration, we can use Eq. (7.8a) and Evaluate Numerically to find the number of times the record turns while it’s slowing down.

  The record turns about 2.8 times while it’s slowing down.

  When the angular acceleration is not constant, you must use calculus to describe the object’s rotational motion. The angular velocity

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