Question

in the figure, point p moves at a constant rate along the unit circle. complete the sentence below. if the angular speed of point p is 1 radian per second, then p will move around the entire circle in sec. if the angular speed of point p is 1 radian per second, then p will move around the entire circle in sec. (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the total angle of a circle

The total angle around a unit - circle is $2\pi$ radians.

Step2: Use the formula for time

We know that angular speed $\omega=\frac{\theta}{t}$, where $\omega$ is the angular speed, $\theta$ is the angle traversed, and $t$ is the time. Given $\omega = 1$ radian per second and $\theta=2\pi$ radians. Rearranging the formula for $t$, we get $t=\frac{\theta}{\omega}$.

Step3: Calculate the time

Substitute $\theta = 2\pi$ radians and $\omega = 1$ radian per second into the formula $t=\frac{\theta}{\omega}$. So, $t = 2\pi$ seconds.

Answer:

$2\pi$