Answer:13 revolution
Step-by-step explanation:
Given data
Wheel initial angular velocity[tex]\left ( \omega \right ) [/tex]=18 rad/s
Contant angular deaaceleration[tex]\left ( \alpha \right )[/tex]=2[tex]rad/s^2[/tex]
Time required to stop wheel completely=t sec
[tex]\omega =\omega_0 + \aplha t[/tex]
0 =18 +[tex]\left ( -2\right )t[/tex]
t=9 sec
Therefore angle turn in 9 sec
[tex]\theta [/tex]=[tex]\omega_{0} t[/tex]+[tex]\frac{1}{2}[/tex][tex]\left ( \alpha\right )t^{2}[/tex]
[tex]\theta [/tex]=[tex]18\times 9[/tex]+[tex]\frac{1}{2}[/tex][tex]\left ( -2\right )\left ( 9\right )^2[/tex]
[tex]\theta [/tex]=81rad
therefore no of turns(n) =[tex]\frac{81}{2\times \pi}[/tex]
n=12.889[tex]\approx [/tex]13 revolution
