Angular Displacement

2 Key excerpts on "Angular Displacement"

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  eBook - ePub

  Biomechanics For Dummies

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

    (Publisher)

  However, angular distance is commonly used to describe the full- or partial-body rotations that occur in sports like diving and gymnastics. When a diver leaves the board upright and completes a forward somersault to enter the water headfirst, the dive is described as a one and a half, with one and a half referring to the number of revolutions completed. The one is the full revolution for the diver to rotate in the air to the head up position, and the half is the incomplete revolution for the diver to rotate to the head down position to enter the water. Angular Displacement Angular Displacement is the angle formed between the initial position of the body and the final position of the body. That is, Angular Displacement is the net change in position of an angle. Angular Displacement is represented with Δθ, with Δ (delta) the symbol for “change in.” Δθ is calculated as θ f – θ i, where θ f is the final angle (the angle at the end of the phase being analyzed) and θ i is the initial angle (the angle at the start of the phase being analyzed). The units for Angular Displacement are degrees or radians, depending on the units used to measure the angles. Δθ is a vector quantity, so both the magnitude (how much the angle changes) and the direction (which way the angle changes) are reported. Angular direction is specified relative to the hands on a clock. By definition, the negative direction is clockwise (the direction the clock hands rotate), and the positive direction is counterclockwise (opposite to the direction the hands rotate). Look again at the change in the relative angle of the knee joint as shown in Figure 9-4. At the start position, indicated with θ 1, the knee is straight, a knee angle of 180 degrees. The knee is then bent (flexed) to position θ 2, a knee angle of 90 degrees, and finally straightened (extended) to position θ 3, a knee angle of 135 degrees

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  eBook - ePub

  Doing Physics with Scientific Notebook

  A Problem Solving Approach

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

    (Publisher)

  Chapter 7

  Circular Motion

  Many real-life motions include rotation. Merry-go-round riders move in circular paths, and the Earth rotates daily as it orbits the Sun in a nearly circular orbit. Tires and axles rotate as a car moves, and thrown and batted baseballs usually spin.

  We could use an object’s x and y coordinates to keep track of its position is it moves in a circle. It is easier to use the circle’s radius (R) and the angle (θ) the object makes with the center of the circle and the x-axis (see Figure 7.1a ). This coordinate system has the radial direction along the circle’s radius, and the tangential direction is along the motion, perpendicular to the radius. The positive radial direction is “In” toward the center of the circle, and the negative radial direction is “Out” away from the center. The positive tangential direction is usually counterclockwise, and negative points clockwise.

  Figure 7.1a

  Angular Position

  The Angular Displacement is the change in the object’s angular position (Δθ).

  (7.1)

  The arc length s is the object’s displacement as it moves along the circle from θ0 to θ. When Δθ is positive, the net change in the object’s angular position is counterclockwise (see Figure 7.1b ) and it’s negative when the net change in angular position is clockwise.

  Figure 7.1b

  Angular Displacement

  The ratio in Eq. (7.1) defines a unit called the radian, the standard unit for angles that SNB denotes rad and lists under Plane Angle in the Unit Name dialog box. The radian is a dimensionless unit, but you can think of it as a “meter-per-meter”. It’s a meter of displacement along the circular path per meter of radial distance from the circle’s center.

  The radian is one of three units for the Angular Displacement, along with degrees and revolutions. For one complete revolution, the arc length is the circle’s circumference (s = 2πR) so Eq. (7.1) tells us there are 2π rad in one revolution.

  SNB has two degree symbols but revolutions are not included in its built-in units. To create a user-defined unit, see Chapter 1 or SNB

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