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Question
A flywheel rotates with uniform angular acceleration. If its angular velocity increases from `20pi` rad/s to `40pi` rad/s in 10 seconds. Find the number of rotations in that period.
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Solution
Given,
Initial angular velocity ω0 = 20 π rad/s
Final angular velocity ω = 40 π rad/s
Time t = 10 s
Solution:
Angular acceleration α = `(ω−ω_0)/t` = `(40π –20π)/10`
α = 2π rad/s2
According to the equation of motion for rotational motion
`theta = omega_0t + 1/2alphat^2 = 20pi xx 10 + 1/2 2pi xx 100 = 300pi` rad
The number of rotations = n = `theta/(2pi)`
n = `(300pi)/(2pi)` = 150 rotations.
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