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 π radians per second, then the linear speed is ____ unit(s) per sec. if the angular speed of point p is π radians per second, then the linear speed is □ unit(s) per 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 linear - angular speed formula

The formula relating linear speed \(v\), angular speed \(\omega\), and radius \(r\) is \(v = r\omega\).

Step2: Identify the radius of the unit circle

For a unit circle, the radius \(r = 1\) unit.

Step3: Substitute the values of \(r\) and \(\omega\)

Given \(\omega=\pi\) radians per second and \(r = 1\) unit, we substitute into the formula \(v=r\omega\). So \(v=1\times\pi=\pi\).

Answer:

\(\pi\)