Find out the answer to "A motor gives gear A an angular acceleration..."

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Wanda Kane

Answered question

2022-01-10

A motor gives gear A an angular acceleration of $α_{A} = (4 t^{3}) rad / s^{2}$ , where t is in seconds. If this gear is initially turning at $(ω_{A})_{0} = 20 r a d / s$ , determine the angular velocity of gear B when t=2 s.

Answer & Explanation

David Clayton

Beginner2022-01-11Added 36 answers

Angular motion of gear A
$∵ α = \frac{d ω}{d t}$
$d ω = α d t$
$∵ \int_{ω 0}^{ω A} d ω_{A} = \int_{0}^{t} α_{A} d t = \int_{0}^{t} 4 t^{3} d t$
$∵ ω_{A} = t^{4} + 20 A t t = 2 s$
$ω_{A} = {(2)}^{4} + 20 = 36 r a \frac{d}{d}$
Since the crush connected to the shaft by a non slip belt.
$ω_{B} r_{B} = ω_{A} r_{A}$
$ω_{B} = \frac{r_{A}}{r_{B}} ω_{A}$
$= \frac{0.15}{0.05} (36)$
$ω_{B} = 12 r a d / s c u r v e \Rightarrow$
The finally answer is
$ω_{B} = 12 r a d / s c u r v e \Rightarrow$

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