1.

A uniform disc of mass m and radius R is given a velocity v_(0) and angular velocity omega_(0) as shown and released of a fixed horizontal surface. Only the x length of the surface is rough. Find the minimum value of x (in metres) so that disc starts pure rolling. Use (omega_(0)^(2)R^(2))/(72mug)=1m

Answer»


Solution :`(momega_(0)R^(2))/2+(mR^(2))/2 omega_(0)=momega_(0)R^(2)+(mR^(2))/2OMEGA`
`impliesomega_(0)=3/2omegaimpliesomega=(2omega_(0))/3`
`implies v=omegaR=2/3omega_(0)R=(4v_(0))/3`
`=(16v_(0)^(2))/9=v_(0)^(2)+2mugx`
`2mugx=(7v_(0)^(2))/9impliesx=(7v_(0)^(2))/(18mug)=(7omega_(0)^(2)R^(2))/(72mug)=7m`


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