Answer:
Angular velocity of tire [tex]\approx 66.67\ s^{-1}[/tex]
Explanation:
Given:
Diameter of tire of an automobile =75.0 cm
Linear velocity of automobile = 90.0 km/hr
To find angular velocity of tire.
Diameter of tire in meters = [tex]75\ cm \times \frac{1\ m}{100\ cm}= 0.75\ m[/tex]
Radius of tire = [tex]\frac{1}{2}\times diameter=\frac{1}{2}\times 0.75\ m = 0.375\ m[/tex]
Linear velocity in meters per second = [tex]\frac{90\ km}{1\ hr}\times \frac{1000\ m}{1\ km}\times \frac{1\ hr}{3600\ s}= 25\ m/s[/tex]
Angular velocity [tex]\omega[/tex] is given by :
[tex]\omega=\frac{v}{r}[/tex]
where [tex]v[/tex] represents linear velocity and [tex]r[/tex] represents radius of tire.
Plugging in values.
[tex]\omega=\frac{25\ m/s}{0.375\ m}[/tex]
∴ [tex]\omega=66.666 s^{-1}\approx 66.67\ s^{-1}[/tex] (Answer)
