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 (square) sec (simplify your answer. type an exact answer, using (pi) as needed. use integers or fractions for any numbers in the expression )

Explanation:

Step1: Recall the angle of a full - circle

The angle measure of a full - circle in radians is $2\pi$.

Step2: Use the angular speed formula

The formula for angular speed $\omega=\frac{\theta}{t}$, where $\omega$ is angular speed, $\theta$ is the angle of rotation, and $t$ is time. We know $\omega = 1$ radian per second and $\theta=2\pi$ radians. Rearranging the formula for $t$ gives $t=\frac{\theta}{\omega}$.

Step3: Substitute values

Substitute $\theta = 2\pi$ and $\omega = 1$ into the formula $t=\frac{\theta}{\omega}$. So $t=\frac{2\pi}{1}=2\pi$.

Answer:

$2\pi$