Figure shows a plank of mass m moving at speed u on a smooth surface. A spinning ball (sphere) of mass m and radius r normally strikes it at speed v. The friction coefficient between ball and upper surface of plank is μ $$=$$ $$0.5$$ and coefficient of restitution is e $$=$$ $$0.5$$. Find the angular velocity of sphere just after collision.

Question

Figure shows a plank of mass m moving at speed u on a smooth surface. A spinning ball (sphere) of mass m and radius r normally strikes it at speed v. The friction coefficient between ball and upper surface of plank is μ $$=$$ $$0.5$$ and coefficient of restitution is e $$=$$ $$0.5$$. Find the angular velocity of sphere just after collision.

Infinity Learn · Accepted Answer

As shown in figure if we write impulse $$=$$ change in momentumequations  mu−$$J2=mv2$$                 mv−$$J1=$$−$$mv2$$ ⇒$$J1=32mv$$                 $$0+J2=mv1$$⇒$$v1=32$$μ$$v=34vvelocity$$ of ball $$vball=(v/2)2+(3v/4)2=134vwe$$ also have  $$25mr2$$ω−$$J2r=25mr2$$ω$$125mr2$$ω−μ$$32mvr==25mr2$$ω$$1$$ω$$1=154$$μvr

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