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Determine the stopping location of the prize wheel. At this moment it is centered on the number 11. It is spinning at a rate of 124.40 rpm. It is slowing at a rate of 1.400 rad/s/s.

Predict the time the wheel will remain spinning, the angular displacement it will go through, and then use this to predict the number on which the wheel will stop. To be safe, you will also get one number the right and to the left of the number you chose.

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Answer:

The wheel spins for 11.43s. The number cannot be determined.

Explanation:

We know that initial velocity is 124.4 rpm = 13.027137522 rad/s, acceleration is -1.14 rad/s^2, and final velocity is assumed to be 0 rad/s. We are asked to find t and displacement. We use the equation [tex]\omega=\omega_0+\alpha t[/tex] where [tex]\omega=0 rad/s[/tex], [tex]\omega_0=13.027 rad/s[/tex], [tex]\alpha=-1.14rad/s^2[/tex], and [tex]t=?[/tex].

Rearrange the equation to obtain [tex]\frac{\omega-\omega_0}{\alpha}=t[/tex]. Plug in the numbers and solve to obtain [tex]t=11.43s[/tex].

The number of the wheel cannot be determined as we do not know the placement of numbers on the wheel.

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