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, ω0=600rev∕min To convert to radians per second: ω0=600×‌
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=20πrad∕s Angular deceleration, α=−2rad∕s2 Final angular velocity, ω=0rad∕s Find: Number of revolutions, N Solution: Using the angular kinematic equation: ω2=ω02+2αθ Plugging in the given values: 0=(20π)2+2(−2)θ Simplify: 0=400π2−4θ Rearrange to solve for θ : 4θ=400π2θ=100π2 Relate θ to revolutions: Since θ=2πN, 2πN=100π2 Solve for N : N=‌