Curvilinear Motion of Particle Flashcards
If acceleration is a function of velocity, how can we find the velocity as a function of time?
dv / dt = f(v)
dv / f(v) = dt
If we then integrate both sides, using the initial and current times and velocities, we can then find the velocity as a function of time.
If acceleration is a function of position , how can we find the position as a function of time?
a = g(x) = dv / dt
a = v (dv/dx) = g(x)
v dv = g(x) dx
If we then integrate both sides, we can then find that dx / dt = h(x) where h(x) is the velocity as a function of position.
If we then integrate it again, we can then rearrange the equation again
dx / h(x) = dt
Finally, we can integrate again to find the position as a function of time
What is the average speed of a point moving between two points under curvilinear motion?
Delta s / Delta t
How can we represent differentials specifically for curvilinear motion?
Dot
This is when there is a dot above the object that is being differentiated:
.
s = The differentiation of displacement = Velocity
What is the angular velocity of a line which passes through point O on a reference plane?
Angular Velocity is the time derivative of the angle travelled
What direction does the angular velocity act?
It acts perpendicular to the reference plane and it’s orientated the same way a right screw would advance as you rotate through the angle theta
Remember to use the right hand screw rule (Wrapping your fingers into a fist in the direction of motion)
What is the angular acceleration?
The time derivative of the angular velocity
What is the angular acceleration?
The time derivative of the angular velocity
What is the time derivative of a vector V rotating at an angular velocity of Omega?
dV / dt = The time derivative of V over small sections + the cross product of omega and V
This allows us to then find out the derivative of the vector itself, and then adding the impact of the rotation
