QuestionIf a ball travels around a circle of radius 4 m in 1.5 minutes, what is the angular spee of the ball? a) $\frac{\pi}{45}$ radians $/ \mathrm{s}$ b) $\frac{2 \pi}{45}$ radians $/ \mathrm{s}$ c) $\frac{\pi}{30}$ radians $/ \mathrm{s}$ d) $\frac{2 \pi}{1.5}$ radians $/ \mathrm{s}$

Studdy Solution
Angular speed is defined as the angle in radians covered per unit time. Since the ball covers the entire circumference, it travels $2\pi$ radians in $90 \, \text{seconds}$.
$$\text{Angular speed} = \frac{2\pi \, \text{radians}}{90 \, \text{seconds}}$$ $$\text{Angular speed} = \frac{\pi}{45} \, \text{radians per second}$$
The angular speed of the ball is:
$$\boxed{\frac{\pi}{45} \, \text{radians per second}}$$