Angular Impulse
Angular impulse is a measure of the rotational motion of an object, calculated as the product of the torque applied to an object and the time over which it is applied. It represents the change in angular momentum of the object and is important in understanding how forces cause rotational motion.
5 Key excerpts on "Angular Impulse"
- Paul Grimshaw, Neil Fowler, Adrian Lees, Adrian Burden(Authors)
- 2007(Publication Date)
- Routledge(Publisher)
...Angular acceleration is defined as the rate of change of angular velocity and is calculated by angular velocity (final – initial) divided by the time taken. Clockwise and anti-clockwise rotation Clockwise rotation is movement in the same direction as the hands of a clock (i.e., clockwise) when you look at it from the front. Clockwise rotation is given a negative symbol (−ve) for representation. Anti-clockwise rotation is the opposite movement to clockwise rotation and it is given a positive symbol (+ve) for representation. Absolute and relative angles An absolute angle is the angle measured from the right horizontal (a fixed line) to the distal aspect of the segment or body of interest. A relative joint angle is the included angle between two lines that often represent segments of the body (i.e., the relative knee joint angle between the upper leg (thigh) and the lower leg (shank)). In a relative angle both elements (lines) that make up the angle can be moving. Included angle and vertex An included angle is the angle that is contained between two lines that meet or cross (intersect) at a point. Often these lines are used to represent segments of the human body. The vertex is the intersection point of two lines. In human movement the vertex is used to represent the joint of interest in the human body (i.e., the knee joint) Angular motion Angular motion is rotatory movement about an imaginary or real axis of rotation and where all parts on a body (and the term body need not necessarily be a human body) or segment move through the same angle. Angular kinematics describes quantities of angular motion using such terms as angular displacement, angular velocity and angular acceleration. Fig. A3.1 identifies two examples of angular motion in more detail. Angular distance or displacement (scalar or vector quantity) is usually expressed in the units of degrees (where a complete circle is 360 degrees)...
eBook - ePubBiomechanics of Human Motion
Applications in the Martial Arts, Second Edition
- Emeric Arus, Ph.D.(Authors)
- 2017(Publication Date)
- CRC Press(Publisher)
...More precisely, the angular speed tells us the change in angle per unit of time, which is measured in radians/s. Angular speed can also be measured in degrees, for example, 360 o /s. Even if the term angular speed is equivalent to rotational velocity, there is a difference, which is the rotation (revolution) per minute, for example, 60 rpm. Angular speed represents the magnitude of angular velocity. The angular velocity, whose sign is also a Greek letter omega (ω), is a vector quantity; that is why in most physics books or other books, the authors use the terms angular velocity and angular speed interchangeably. The magnitude of angular velocity can be described in two terms. One is the average angular velocity, which represents the angular displacement of an object between two points of an angle such as θ 1 and θ 2 at the time intervals t 1 and t 2, respectively. Then, the equation for average angular velocity is = (θ 2 -θ 1 / t 2 - t 1)= (∆θ/∆ t); the other term for the magnitude is the instantaneous angular velocity, which is the limit of the magnitude ratio as Δ t approaches 0. The formula is: ω = lim as Δ t → 0 Δθ/Δ t = dθ/d t, both and ω being measured in m/s. To find out the average angular acceleration and the instantaneous angular acceleration, we proceed in an analogous fashion to linear velocities and accelerations. The average angular acceleration () of a rotating body in the interval from t 1 to t 2 can be defined using the following formula, where ω represents the instantaneous angular velocities. The formula for average angular acceleration =ω 2 -ω 1 / t 2 - t 1 = ∆ω/∆ t,and the instantaneous angular acceleration α = lim as Δ t → 0 Δω/Δ t = dω/d t, both and α being measured in rad/s 2. Speaking about angular motion, we should mention two different and important accelerations. One of these is the so-called radial component of the linear acceleration that is named radial acceleration, also called centripetal acceleration...
eBook - ePub- W. Bolton(Author)
- 2015(Publication Date)
- Routledge(Publisher)
...Chapter 5 Angular motion 5.1 Introduction This chapter is concerned with describing angular motion, deriving and using the equations for such motion and relating linear motion of points on the circumference of rotating objects with their angular motion. The term torque is introduced. 5.1.1 Basic terms The following are basic terms used to describe angular motion. Angular displacement The angular displacement is the angle swept out by the rotation and is measured in radians. Thus, in Figure 5.1, the radial line rotates through an angular displacement of θ in moving from OA to OB. One complete rotation through 360° is an angular displacement of 2 π rad; one quarter of a revolution is 90° or π /2 rad. As 2 π rad 5 360°, then 1 rad 5 360°/2 π or about 57°. Figure 5.1 Angular motion 2 Angular velocity Angular velocity ω is the rate at which angular displacement occurs, the unit being rad/s. 3 Average angular velocity The average angular velocity over some time interval is the change in angular displacement during that time divided by the time...
eBook - ePub- A. D. Johnson(Author)
- 2017(Publication Date)
- Routledge(Publisher)
...Angular motion equivalent parameters need to be inserted as follows: Linear motion Angular. motion v = s t (2.1) ω = θ t (2.6) v 2 = v 1 + a t (2.2) ω 2 = ω 1 + α t (2.10) s = (v 1 + v 2) t 2 (2.3) θ = (ω 1 + ω 2) t 2 (2.11) s = v 1 t + 1 2 a t 2 (2.4) θ = ω 1 t + 1 2 α t 2 (2.12) v 2 2 =[--=PLGO-SEPARATOR=. --]v 1 2 + 2 a s (2.5) ω 2 2 = ω 1 2 + 2 α θ (2.13) Example 2.15 A wheel, initially at rest, is subjected to a constant angular acceleration of 2.5 rad/s 2 for 60s. Find: the angular velocity attained; the number of revolutions made in that time. Solution The angular velocity can be found using equation (2.10), but α = 2.5rad/s 2, f = 60s, so ω 2 = ω 1 + α t = 0 + (2.5 × 60) = 150 rad/s The angular displacement can be found using equation (2.12) : θ = ω 1 t + 1 2 α t 2 so that θ = 2.5 × 60 2 2 = 4500 rad To convert the angular displacement to revolutions it is recognized that one revolution represents 2π rad: n = 4500 2 π = 716 rev Example 2.16 A wheel initially has an angular velocity of 50 rad/s. When brakes are applied the wheel comes to rest in 25 s. Find the average retardation. Solution The angular retardation can be found using equation (2.10) : ω 2 = ω 1 + α t but ω 1 = 50 rad/s, ω 2 = 0, t = 25 s, so that 0 = 50 + (α × 25) giving α = − 50 25 = − 2rad/s 2 Example 2.17 A drum starts from rest and attains a rotation of 210 rev/min in 6.2 s with uniform acceleration. A brake is then applied which brings the drum to rest in a further 5.5 s with uniform retardation. Find the total number of revolutions made by the drum. Solution The total number of revolutions can be found by using equation (2.11) : θ = (ω 1 + ω 2) t 2 Fig. 2.17 Consider, initially, area A under the velocity–time graph (Figure 2.17)...
eBook - ePub- J Jones, J Burdess, J Fawcett(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
...If the positions of Q and P are x Q, y Q and x P, y P respectively, as shown in Fig. 6.15, then the absolute angular momentum about the point Q is given by F IG. 6.15 If we now differentiate eqn (6.37) with respect to time we obtain Since and represent the components of the external force F applied to the particle, eqn (6.38) may be rewritten The right hand side of this equation is the moment M Q of the applied force F about the point Q. The rate of change of the absolute angular momentum about any point Q is equal to the moment of the applied force about Q. When eqn (6.39) is integrated with respect to time over the interval t 1 to t 2 we have The quantity is called the Angular Impulse of the applied force about the point Q and is equal to the change in the absolute angular momentum of the particle about Q. It should be understood that, in general, the Angular Impulse about Q is not equal to the moment of the linear impulse about Q. Since x P and y P are functions of time Systems of particles Let us suppose we have a closed system of particles contained within a boundary S as shown in Fig. 6.16(a). The total absolute angular momentum of the whole system about the fixed point Q may be obtained directly from eqns (6.34) and (6.37) as the sum of the individual absolute angular momenta about Q and is given by F IG. 6.16 The quantities written with the suffix i, relate to the typical particle P f, as shown in Fig...
