Question

We are going to derive the virial theorem that is valid for any periodic orbit of a particle.

(a) Find the time derivative of the quantity g(t) _____.

(a) with respect to position
(b) with respect to time
(c) with respect to velocity
(d) with respect to momentum

Answer 1

To calculate the velocity of a particle, the time derivative of the position function is taken. Similarly, taking the time derivative of the velocity function yields the particle's acceleration, both of which are vector quantities in dynamics.

Step-by-step explanation:

The virial theorem is a result in dynamics dealing with the average properties of stable systems in equilibrium. In physics problems, it's common to calculate various derivatives of motion-related functions. To find the velocity of a particle you would take the time derivative of its position function, đ(t). For example, given the position đ(t) = A (cos wtî + sin wtķ), the velocity — found by taking the time derivative — would be v(t) = dđ/dt which encompasses the change in position with respect to time.

When examining the motion of particles, kinematic equations derived from integral calculus are frequently used. These equations are also important when discussing the time derivative of a position function, which gives us the velocity function. Likewise, the time derivative of the velocity function provides the acceleration of the particle, all being vector quantities.