You give an orbiting satellite a command to rotate through an angle given by
$\theta$ = at + bt² - ct⁴
Where a, b, and c are constants and $\theta$ is in radians if t is in seconds. What is the angular acceleration of this satellite at time t?

Question

You give an orbiting satellite a command to rotate through an angle given by

\theta

= at + bt² - ct⁴
Where a, b, and c are constants and

\theta

is in radians if t is in seconds. What is the angular acceleration of this satellite at time t?

Quizplus · Accepted Answer

The given equation can be rewritten as:

F1F1F1S1F1F1F10 = (a - ctS1U1P14)s + btS1U1P12

Taking the first derivative of the equation with respect to time, we get:

angular velocity = d(F1F1F1S1F1F1F10)/dt = (bS1U1P12 - cS1U1P14)

Taking the second derivative of the equation with respect to time, we get:

angular acceleration = d²(F1F1F1S1F1F1F10)/dt² = 2bS1U1P0 - 12cS1U1P12S1S1P0

Therefore, the answer is D, which is 2b - 12ctS1U1P12 S1S1P0.

You Give an Orbiting Satellite a Command to Rotate Through θ\thetaθ