Given data
*The given radius of the wheel is r = 30.0 cm = 0.30 m
*The given angle of the wheel rotates in 1.00 s is
[tex]\theta=178.0\text{ rad}[/tex]*The angular velocity of the wheel is
[tex]\omega=178.0\text{ rad/s}[/tex]The formula for the linear speed of a point on the wheel's rim is given as
[tex]v=r\omega[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=(0.30)(178.0) \\ =53.4\text{ m/s} \end{gathered}[/tex]Hence, the linear speed of a point on the wheel's rim is v = 53.4 m/s
The formula for the wheel's frequency of rotation is given as
[tex]\begin{gathered} \omega=2\pi f \\ f=\frac{\omega}{2\pi} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} f=\frac{178.0}{2\times3.14} \\ =28.34\text{ Hz} \end{gathered}[/tex]Hence, the wheel's frequency of rotation is f = 28.34 Hz
