Answer:
[tex]\Delta \theta=19.44\ rad[/tex]
Explanation:
We just have to calculate what angular displacement a ball with an average angular velocity of 290 rev/min experiments in 0.64s. By definition, angular velocity [tex]\omega[/tex] is the angular displacement [tex]\Delta \theta[/tex] divided by the time elapsed:
[tex]\omega=\frac{\Delta \theta}{\Delta t}[/tex]
Since [tex]1\ rev=2\pi \ rad[/tex] and [tex]1\ min=60\ s[/tex], we can covert:
[tex]\omega=290\ rev/min=\frac{290\ rev}{min}(\frac{1\ min}{60s})(\frac{2\pi \ rad}{1\ rev})=30.37\ rad/s[/tex]
Where the terms between parenthesis are equal to 1, so they just change the units. Then for our values we have:
[tex]\Delta \theta=\omega \Delta t=(30.37\ rad/s)(0.64s)=19.44\ rad[/tex]
