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There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
For rod length 6" and crank radius 2" (as shown in the example graph below), numerically solving the acceleration zero-crossings finds the velocity maxima/minima to be at crank angles of ±73.17615°.
This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50 % of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90 %, 15 seconds to ...
Consequently, the acceleration is the second derivative of position, [7] often written . Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. [9]: 1 Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to ...
Timing diagram over one revolution for angle, angular velocity, angular acceleration, and angular jerk. Consider a rigid body rotating about a fixed axis in an inertial reference frame. If its angular position as a function of time is θ(t), the angular velocity, acceleration, and jerk can be expressed as follows:
Acceleration has the dimensions of velocity (L/T) divided by time, i.e. L T −2. The SI unit of acceleration is the metre per second squared (m s −2); or "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second.
Hence the change in proper-velocity w=dx/dτ is the integral of proper acceleration over map-time t i.e. Δw = αΔt for constant α. At low speeds this reduces to the well-known relation between coordinate velocity and coordinate acceleration times map-time, i.e. Δv=aΔt.
Angular velocity: the angular velocity ω is the rate at which the angular position θ changes with respect to time t: = The angular velocity is represented in Figure 1 by a vector Ω pointing along the axis of rotation with magnitude ω and sense determined by the direction of rotation as given by the right-hand rule.