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Wheel A of radius 10 cm is coupled by a ...

Wheel A of radius 10 cm is coupled by a belt B to wheel C of radius 30 cm as shown in figure. Wheel A increases its angular speed from rest at a uniform rate of `1.57rad//s^(2)`. Determine the time for wheel C to reach a rotational speed of 100 rev/min assuming that the belt does not slip.

Text Solution

Verified by Experts

As the belt does not slip `v_(A)=v_(C)`
i.e. `r_(A)omega_(A)=r_(C)omega_(C)" "` [as `v=r omega`]
Here `r_(A)=10cm" "r_(C)=30cm`
and `omega_(c)=(2pixx100/60)` rad/s
so `10 omega_(A)=30xx(2pixx100)/60`
i.e. `omega_(A)=10pi` rad/s
No from 1st equation of rotational motion i.e. `omega=omega^(0)+alphat`
`t=(omega)/(alpha)` [as `omega_(0)=theta`]
i.e. `t=(10xxpi)/1.57= 20`sec
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