An electric motor rotating a workshop grinding wheel at a rate of 215 rev/min is switched off. Assume constant angular deceleration of magnitude 2.07 rad/s 2 . Through how many revolutions does the wheel turn before it finally comes to rest

19.49 rev

Explanation:

Using,

ω₂² = ω₁²+2αθ Equation 1

Where ω₂ = Final angular velocity, ω₁ = Initial angular velocity, α = angular deceleration, θ = number of revolution.

make θ the subject of the equation

θ = (ω₂²- ω₁²)/2α Equation 2

Given: ω₂ = 0 rad/s (comes to rest), ω₁ = 215 rev/min =  rad/s, α = -2.07 rad/s²(deceleration) = -2.07(572.957) = -1186.02 rev/min²

Substitute into equation 2

θ = (0²-215²)/2(-1186.02)

θ = -46225/-2372.04

θ = 19.49 rev

Hence the wheel makes 19.49 rev

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