The angular velocity is 2512 rad/min
Explanation:
The angular velocity of a rotating object is equal to the rate of change of the angular displacement:
[tex]\omega = \frac{\Delta \theta}{\Delta t}[/tex]
where
[tex]\Delta \theta[/tex] is the angular displacement
[tex]\Delta t[/tex] is the time elapsed
In this problem, we know that the wheels are turning 400 times a minute. This means that:
The angular displacement corresponding to 1 revolution is [tex]2\pi[/tex], so 400 revolutions correspond to an angle of
[tex]\Delta \theta = 400 \cdot 2 \pi = 800 \pi[/tex]
Moreover, the time interval is
[tex]\Delta t= 1min[/tex]
Therefore, the angular velocity of the wheel is
[tex]\omega=\frac{800 \pi}{1}=2512 rad/min[/tex]
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