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A 60 cm diameter wheel accelerates from rest at a rate of 7 rad/s2. How long does it take for the wheel to turn through 14 rotations?.

User Tinisha
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1 Answer

1 vote
Rotational (angular) acceleration:
α = 7 rad/s²

Time evolution:
i) angular velicty: ω(t) = αt
(Same approach as the motion of uniform acceleration)
with rest condition: ω(0) = 0

ii) Rotation: θ(t) = ½αt²
with setting initial angle : θ(0) = 0

We need to find t for θ(t) = 14
½αt² = (7/2)t² = 14

→ t² = 28 ÷ 7 = 4

∴ t = 2

It takes 2 seconds for 14 rotations.

The diameter is not important information for this problem.
User Stefan Wittwer
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7.5k points