A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from 20π rad s-1 to 40π rad s-1 in 10 seconds. How many rotations did it make in this period?

Question

A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from 20π rad s-1 to 40π rad s-1 in 10 seconds. How many rotations did it make in this period? (A) 80 (B) 100 (C) 120 (D) 150

Tardigrade Admin · Accepted Answer

As ω2=ω1 +α t : :: ∴ : 40π + 20π + α ×10 or α = 2π rad s-2 From, ω22 -ω12 = 2 α θ (40π)2 -(20π)2 =2 ×2πθ or θ = (1200π2/4π) =300π No. of rotations completed = (θ/2π)=(300π/2π)=150

Q. A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20 π r a d s^{- 1}$ to $40 π r a d s^{- 1}$ in 10 seconds. How many rotations did it make in this period?

80

100

120

150

As $ω_{2} = ω_{1} + α t ∴ 40 π + 20 π + α \times 10$ or $α = 2 π r a d s^{- 2}$
From, $ω_{2}^{2} - ω_{1}^{2} = 2 α θ$
$(40 π)^{2} - (20 π)^{2} = 2 \times 2 π θ$
or $θ = \frac{1200 π ^{2}}{4 π} = 300 π$
No. of rotations completed $= \frac{θ}{2 π} = \frac{300 π}{2 π} = 150$

Q. A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from 20πrads−1 to 40πrads−1 in 10 seconds. How many rotations did it make in this period?

80

100

120

150

As ω2​=ω1​+αt∴40π+20π+α×10 or α=2πrads−2 From, ω22​−ω12​=2αθ (40π)2−(20π)2=2×2πθ or θ=4π1200π2​=300π No. of rotations completed =2πθ​=2π300π​=150

Q. A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20 π r a d s^{- 1}$ to $40 π r a d s^{- 1}$ in 10 seconds. How many rotations did it make in this period?

As $ω_{2} = ω_{1} + α t ∴ 40 π + 20 π + α \times 10$ or $α = 2 π r a d s^{- 2}$
From, $ω_{2}^{2} - ω_{1}^{2} = 2 α θ$
$(40 π)^{2} - (20 π)^{2} = 2 \times 2 π θ$
or $θ = \frac{1200 π ^{2}}{4 π} = 300 π$
No. of rotations completed $= \frac{θ}{2 π} = \frac{300 π}{2 π} = 150$