Circular Motion

We need to determine the number of revolutions a wheel makes before coming to a stop. Here's the breakdown of the solution: Initial angular velocity, $\omega_0=600\ \text{rev}/\text{min}$To convert to radians per second:$\omega_0=600\times\frac{2\pi}{60}=20\pi\ \text{rad}/\text{s}$Angular deceleration, $\alpha=-2\ \text{rad}/\text{s}^2$Final angular velocity, $\omega=0\ \text{rad}/\text{s}$Find:Number of revolutions, $N$Solution:Using the angular kinematic equation:$\omega^2=\omega_0^2+2\alpha\theta$Plugging in the given values:$0=(20\pi)^2+2(-2)\theta$Simplify:$0=400\pi^2-4\theta$Rearrange to solve for $\theta$ :$4\theta=400\pi^2\theta=100\pi^2$Relate $\theta$ to revolutions:Since $\theta=2\pi N$,$2\pi N=100\pi^2$Solve for $N$ :$N=\frac{100\pi^2}{2\pi}N=50\pi$Assuming $\pi\approx3.14$,$N=50\times3.14=157$