Question

suppose that point p is on a circle with radius r, and ray op is rotating with angular speed ω. complete parts (a) through (c) for the given values of r, ω, and t. r = 4 in., ω = \frac{\pi}{3} radian per min, t = 6 min (a) what is the angle generated by p in time t? θ = radians (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 formula for angle

The formula for the angle $\theta$ generated in time $t$ with angular - speed $\omega$ is $\theta=\omega t$.

Step2: Substitute the given values

We are given that $\omega = \frac{\pi}{3}$ radian per min and $t = 6$ min. Substitute these values into the formula: $\theta=\frac{\pi}{3}\times6$.

Step3: Simplify the expression

$\frac{\pi}{3}\times6 = 2\pi$.

Answer:

$2\pi$