Dynamics and Relativity 2 Flashcards
(7 cards)
Work
work is done when an object is moved against a force through a distance x. work is the dot product of these. for non constant forces, it is the integral of the force ds. For a varying force like spring extension -kx, it can be integrated to achieve work is 1/2kx^2. It also follows conservation of energy
Power
Power is the rate of change of momentum. we can use separation of variables to probe power is work over time, or the dot product of F and v
Conservation of energy
yeah man. Conservative fields are found if independent of path and reversible. and a potential energy equation can be formed. Force is the negative of the rate of change of potential energy. We can integrate the force to get potential.
Momentum and impulse
Force is the rate of change of momentum. Impulse is Ft, and it is the change in momentum. Momentum is conserved in collisions. collisions can be elastic or inelastic. In elastic collisions, conservation of energy can be used in tandem with conservation of momentum.
Angular momentum and torque
Similarly to force and linear momentum, angular momentum is the rate of change of torque. Angular momentum is equal to PXr, where r is the postition vector Or. torque is the cross product of F and r. In the absence of external torques angular momentum is always conserved.
Rotational energy
take 1/2 mv^2 and sub woth v = wr. then define moment of inertia I = mr^2, then ou can add all individual moments of inertia for point particles of negligible radius to get moment of inertia of objects.
Time dilation
FOr light to stay constant at c depending on frame of reference, instead of changing velocity, we can change time intervals or lengh to make the maths work. When somebody is moving relatively to you, light is travelling a longer distance relative to you than to them, but since it cannot move any faster, their time interval must be longer.
