China
Africa
Explore chapters and articles related to this topic
Bohr, Sommerfeld and Old Quantum Mechanics
Published in Caio Lima Firme, Quantum Mechanics, 2022
where a0 is the Bohr radius and v is the linear velocity of the electron. In classical physics, the angular momentum is given by the product of the moment of inertia, I (needed torque to yield angular acceleration), and angular velocity, ω: L=IωI=mr2,ω=v/r,L=mvr
Angular Momentum Equation
Published in Osamu Morita, Classical Mechanics in Geophysical Fluid Dynamics, 2019
In this chapter the third transformation of the equation of motion is performed. The obtained equation is referred to as the angular momentum equation, which relates the changing rate of angular momentum to torque. Angular momentum is the rotational analogue of momentum of a system, while torque is the rotational analogue of force exerting on the system. When no torque is exerting on the system or the total torque is zero, the angular momentum of the system is conserved, which is called the law of angular momentum conservation. At the end of this chapter, statics of a rigid body is discussed for several examples.
Elements of a Classical Control System
Published in Thrishantha Nanayakkara, Ferat Sahin, Mo Jamshidi, Intelligent Control Systems with an Introduction to System of Systems Engineering, 2018
Thrishantha Nanayakkara, Ferat Sahin, Mo Jamshidi
In the previous chapter, we saw that Newton’s equation F=Mx¨ states that the force (N) applied on a mass (kg) is equal to the rate of change of momentum of the mass. The same can be said of rotating systems. The torque τ (N m) applied on a system with moment of inertia Iw (kg m2), is related to the angular acceleration θ¨ (rad/s2), as given by the equation τ = Iwθ¨. Therefore, the rate of change of angular momentum is equal to the torque applied.
Dynamics of a power hacksaw mechanism, contact interaction with the workpiece, and material removal
Published in International Journal of Modelling and Simulation, 2022
Aman Kumar Maini, Anand Vaz, Geneviève Dauphin-Tanguy
The term is the moment of momentum or angular momentum of the crank about its center of mass C2 and expressed in the inertial frame {0}. It clearly represents the cause–effect relationship between the resultant moment acting on the rigid body and its angular momentum. The total torque acting on the rigid body causes a change in its angular momentum. The inertia tensor changes continuously with orientation when expressed in the inertial frame. Similarly, the bond graph of link 3 (connecting rod) can be constructed. Since the points A2 on link 2 and A3 on link 3 are coincident, there is no relative velocity between them. The dynamics of couplings between the two links has been shown in the multibond graph of Figure 6.
Rotation of the thrower-discus system and performance in discus throwing
Published in Sports Biomechanics, 2021
Angular momentum is a measure of the amount of rotation of a system. As a vector, the angular momentum of the thrower-discus system has three independent components representing system rotations about three orthogonal axes: (1) angular momentum of top-to-left or top-to-right rotation about a horizontal axis aligned with the midline of the throwing sector (front-back axis); (2) angular momentum of top-to-front or top-to-back rotation about a horizontal axis aligned with a foul line the throwing ring (left-right axis); and (3) angular momentum of right-to-left or left-to-right rotation about a vertical axis (up-down axis) (Figure 1). These angular momentum components may affect the vacuum flight distance through their relationships with discus speeds. The system angular momentum about the up-down and left-right axes is related to the horizontal speed of the discus, while the angular momentum about the front-back and axis is related to the vertical speed of the discus (Dapena & McDonald, 1989). The angular momentum of the thrower-discus system may also affect the aerodynamic distance through their relationships with discus rotations. The system angular momentum about the up-down axis is related to the discus rotation about its own up-down axis, while the system angular momentum about the front-back axis is related to the discus rotation about its own front-back axis. The rotation of the discus about its up-down axis will increase the gyroscopic stability of the discus during flight and thus gain aerodynamic distance, while the rotation of the discus about its front-back axis may decrease the stability of the discus flight and thus cause it to lose aerodynamic distance (Hubbard & Cheng, 2007; Seo et al., 2012).
Rotational shot put: a phase analysis of current kinematic knowledge
Published in Sports Biomechanics, 2022
Michael Schofield, John B. Cronin, Paul Macadam, Kim Hébert-Losier
Angular momentum is the product of the moment of inertia and angular velocity of a segment, object, or system about an axis (Dapena, 1978). Linear momentum is the product of mass and velocity of a segment, object, or system. Both angular and linear momentum are vector quantities that possess a magnitude and a direction in 3D space. Only two investigations have reported angular and linear momentum, both of which used the same body segment parameters and model for prediction (Byun et al., 2008; Kato, Kintaka, Urita, & Maeda, 2017).