Search results
Results from the WOW.Com Content Network
The velocity of the points X i along their trajectories are = + ˙, where ω is the angular velocity vector obtained from the skew symmetric matrix [] = ˙, known as the angular velocity matrix. The small amount of work by the forces over the small displacements δr i can be determined by approximating the displacement by δr = vδt so ...
The work done by the force F is given by the integral = = = = = , where dr is the differential element along the curve that is the trajectory of P, and v is its velocity. It is important to notice that the value of the work W depends on the trajectory r ( t ) .
Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F ...
Trajectory of a particle with initial position vector r 0 and velocity v 0, subject to constant acceleration a, all three quantities in any direction, and the position r(t) and velocity v(t) after time t. The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical ...
The kinetic energy of an object is equal to the work, or force in the direction of motion times its displacement , needed to accelerate the mass from rest to its stated velocity. Having gained this energy during its acceleration , it maintains this kinetic energy unless its speed changes.
Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path. Unlike other resistive forces, drag force depends on velocity. [ 2 ] [ 3 ] Drag force is proportional to the relative velocity for low-speed flow and is proportional to the velocity squared for high-speed flow.
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
The interpretation of this equation is that the velocity of the particle seen by observers in frame A consists of what observers in frame B call the velocity, namely v B, plus two extra terms related to the rate of change of the frame-B coordinate axes. One of these is simply the velocity of the moving origin v AB. The other is a contribution ...