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A solid body rotest about a stationary a...

A solid body rotest about a stationary axis, so that its angular velocity depends on the rotational angle `phi` as `omega=omega_(0)-kphi` where `omega_(0)` and K are postitive constatns. At the moment `t=0,phi=0` Find the dependence of rotaions angle.

A

`komega_(0)e^(-kt)`

B

`(omega_(0))/(k)e^(-kt)`

C

`(omega_(0))/(k)(1-e^(-kt))`

D

`(k)/(omega_(0))(e-^(kt-1))`

Text Solution

Verified by Experts

(c) `:.`omega=omega_(0)-kphi`
or `(dphi)/(dt)=omega_(0)-kphi`
or `int_(0)^(phi)(dphi)/(omega_(0)-kphi)=int_(0)^(t)dt`
or `(-1)/(k)[ln(omega_(0)-kphi)]_(0)^(phi)=t`
or `ln(omega_(0)-kphi)/(omega_(0))-kt`
`:. phi=(omega_(0))/(k)(1-e^(-kt))`
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