a flywheel increases it's speed from 30 r. p. m to 60 r.p.m in 10seconds.calculate the angular acceleration and no of revolution made by the in these 10seconds
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Explanation:
Given a flywheel increases it's speed from 30 r. p. m to 60 r.p.m in 10 seconds.calculate the angular acceleration and no of revolution made by it in these 10 seconds
- We need to find the angular acceleration and number of revolution.
- So we need to find ω initial and ω final
- So ω i = 30 rpm (rotation per minute)
- = 30 x 2π / 60 rad / sec
- = π rad / sec
- So ω f = 60 rpm
- = 60 x 2π / 60
- = 2π rad / sec
- Also Δt = 10 secs
- Now using uniformly accelerated motion we have
- So ωf = ωi + αΔt
- 2π = π + α (10)
- Or π = 10 α
- Or α = π / 10 rad / s^2
- We need to find the number of revolutions.
- So we have third equation of motion to find theta, so we get
- So ωf^2 – ωi^2 = 2αΔθ
- (2π)^2 – (π)^2 = 2 π / 10 x Δθ
- 3π^2 = π / 5 Δθ
- Or Δθ = 15 rad
- Now number of revolutions n = Δθ / 2π
- = 15 π / 2π
- = 7.5 revolutions.
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Given:
A flywheel increases it's speed from 30 r. p. m to 60 r. p. m in 10sec.
To Find:
Calculate the angular acceleration and no of revolution made by the in these 10sec.
Solution:
since, we know that-
where, is the final angular velocity.
is initial angular velocity.
ω = angular acceleration , t = time
therefore, on putting given values , we get
Now, we know that , each rotation consist of 2π radian.
therefore, no. of revolution made by flywheel in these 10 seconds is
.
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