Question and Answers Forum

All Questions      Topic List

Mechanics Questions

Previous in All Question      Next in All Question      

Previous in Mechanics      Next in Mechanics      

Question Number 52814 by ajfour last updated on 13/Jan/19

Commented by ajfour last updated on 13/Jan/19

$$Initiallyrodwhoseoneendis$$$$pivotedtocentreofdisc,iskept$$$$verticalandreleased,Findv\left(\theta \right).$$$$Frictionissufficientsay,$$$$coefficientis\mu .$$

Commented by tanmay.chaudhury50@gmail.com last updated on 13/Jan/19

$$mg\times \frac{l}{2}(1-cos\theta )=\frac{1}{2}\left(\frac{{ml}^2}{3}\right){\left(w_{rod}\right)}^2+\frac{1}{2}{mV}^2+\frac{1}{2}{MV}^2+\frac{1}{2}\left(\frac{1}{2}{MR}^2\right){\left(w_{disc}\right)}^2$$$$aboveeqnlossoP.E=k.E(rotational+liniear)forbothdiscandrod$$$$$$$$\left(\frac{{ml}^2}{3}\right)w_{rod}=\left(\frac{1}{2}{MR}^2\right)w_{disc}\leftarrow conservationofangularmomentum$$$$\left(\frac{{ml}^2}{3}\right)w_{rod}=\left(\frac{{MR}^2}{2}\right)\left(\frac{V}{R}\right)$$$$w_{rod}=\frac{{MR}^2\times 3}{2\times {ml}^2}\times \frac{V}{R}$$$$w_{rod}=\frac{3M}{2m}\times \left(\frac{RV}{l^2}\right)$$$$mg\times \frac{l}{2}(1-cos\theta )=\frac{1}{2}\left(\frac{{ml}^2}{3}\right)\left(\frac{9M^2}{4m^2}\times \frac{R^2{V}^2}{l^4}\right)+\frac{1}{2}{mV}^2+\frac{1}{2}{MV}^2+\frac{1}{2}\left(\frac{1}{2}{MR}^2\right)\left(\frac{V^2}{R^2}\right)$$$$mg\times \frac{l}{2}(1-cos\theta )=\frac{3}{8}\left(\frac{M^2}{m}\right)\left(\frac{R^2}{l^2}\right)V^2+\frac{1}{2}{MV}^2+\frac{1}{4}{MV}^2$$$$=\frac{3}{8}\left(\frac{M^2}{m}\right)\left(\frac{R^2}{l^2}\right)V^2+\frac{3}{4}{MV}^2$$$$=\frac{3}{4}{MV}^2(1+\frac{1}{2}\times \frac{M}{m}\times \frac{R^2}{l^2})$$$$V^2=\frac{mgl(1-cos\theta )}{2\times \frac{3}{4}M(1+\frac{1}{2}\times \frac{M}{m}\times \frac{R^2}{l^2})}$$$$V^2=\frac{2mgl(1-cos\theta )}{3M(1+\frac{{MR}^2}{2{ml}^2})}$$$$isitok...$$$$$$

Commented by ajfour last updated on 13/Jan/19

$$ishallgothroughsir,letsometime..$$

Commented by tanmay.chaudhury50@gmail.com last updated on 13/Jan/19

$$oksir$$

Commented by tanmay.chaudhury50@gmail.com last updated on 14/Jan/19

$$oksir...$$

Commented by ajfour last updated on 14/Jan/19

$$TanmaySir,ithinkinconservation$$$$ofangularmomentumweshould$$$$alsoincludeMVR..$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com