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Sagot :
We are asked to determine the linear speed given a radius and the number of revolutions per a given amount of time. To do that we will use the following formula:
[tex]v=r\omega[/tex]Where:
[tex]\begin{gathered} r=\text{ radius} \\ \omega=\text{ angular velocity} \end{gathered}[/tex]We need to determine first the angular velocity. To do that we use the quotient between the number of revolutions and the time to do the revolutions. But first, we need to convert 1 revolution into radians. To do that we use the following formula:
[tex]1\text{rev}=2\pi\text{radians}[/tex]Now, we determine the quotient:
[tex]\omega=\frac{2\pi radians}{0.375s}[/tex]Solving the operations:
[tex]\omega=16.76\frac{rad}{s}[/tex]Now, we need to convert the radius from inches into meters. To do that we will use the following conversion factor:
[tex]1m=39.37in[/tex]Multiplying by the conversion factor:
[tex]19.5in\times\frac{1m}{39.37in}=0.495m[/tex]Now we substitute the values in the formula for the velocity:
[tex]v=(0.495m)(19.76\frac{rad}{s})=9.78\frac{m}{s}[/tex]Therefore, the linear speed is 9.78 m/s
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