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Typically, a human's center of mass is detected with one of two methods: the reaction board method is a static analysis that involves the person lying down on that instrument, and use of their static equilibrium equation to find their center of mass; the segmentation method relies on a mathematical solution based on the physical principle that ...
F = total force acting on the center of mass m = mass of the body I 3 = the 3×3 identity matrix a cm = acceleration of the center of mass v cm = velocity of the center of mass τ = total torque acting about the center of mass I cm = moment of inertia about the center of mass ω = angular velocity of the body α = angular acceleration of the body
A special case of the center-of-momentum frame is the center-of-mass frame: an inertial frame in which the center of mass (which is a single point) remains at the origin. In all center-of-momentum frames, the center of mass is at rest , but it is not necessarily at the origin of the coordinate system.
where F ext is the net external force on the body, v rel is the relative velocity of the escaping or incoming mass with respect to the center of mass of the body, and v is the velocity of the body. [3] In astrodynamics, which deals with the mechanics of rockets, the term v rel is often called the effective exhaust velocity and denoted v e. [4]
The resulting equation: ¨ = shows that the velocity = of the center of mass is constant, from which follows that the total momentum m 1 v 1 + m 2 v 2 is also constant (conservation of momentum). Hence, the position R ( t ) of the center of mass can be determined at all times from the initial positions and velocities.
where is the mass of the rigid body; ¯ is the velocity of the center of mass of the rigid body, as viewed by an observer fixed in an inertial frame N; ¯ is the angular momentum of the rigid body about the center of mass, also taken in the inertial frame N; and is the angular velocity of the rigid body R relative to the inertial frame N. [3]
The unit of momentum is the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meters per second (kg⋅m/s). In cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters per ...
Figure 1: Velocity v and acceleration a in uniform circular motion at angular rate ω; the speed is constant, but the velocity is always tangential to the orbit; the acceleration has constant magnitude, but always points toward the center of rotation. Figure 2: The velocity vectors at time t and time t + dt are moved from the orbit on the left ...