A problem by Achal Jain

Level pending

A wheel rotates with constant acceleration of 2.0rad/sec^2, if the wheel starts from rest the number of revolutions it makes in the first 10 seconds will be approximately

24 8 16 32

Achal Jain by Achal Jain , 19, India

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1 solution

Chew-Seong Cheong
Jun 20, 2015

d d t ω ( t ) = 2 ⇒ ω ( t ) = 2 t + c 1 . \dfrac{d}{dt}\omega(t) = 2 \space \Rightarrow \omega(t) = 2t + c_1. \space Since ω ( 0 ) = 0 ⇒ ω ( t ) = d d t θ ( t ) = 2 t \space \omega(0) = 0 \space \Rightarrow \omega (t) = \dfrac {d}{dt}\theta(t) = 2t .

⇒ θ ( t ) = t 2 + c 2 . \Rightarrow \theta (t) = t^2 + c_2. \space Again, since θ ( 0 ) = 0 \space \theta(0) = 0

⇒ θ ( t ) = t 2 ⇒ θ ( 10 ) = 100 rad = 100 2 π = 15.9 ≈ 16 revolutions \Rightarrow \theta(t) = t^2 \space \Rightarrow \theta(10) = 100 \text{ rad} = \dfrac {100}{2\pi} = 15.9 \approx \boxed{16} \text{ revolutions} .

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