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candyq27

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Two identical grinding wheels of mass m and radius r are initially spinning about their centers. Wheel A has an intial angular speed of w, while wheel B has an initial angular speed of 2w. Both wheels are being used to sharpen tools. For both wheels the tool is being pressed against the wheel with a force F directed toward the center of the wheel, and the coefficient of kinetic friction between the wheel and the tool is uk. You are holding the tool firmly so it does not move tangentially to the wheel.

(a) If it takes wheel A a time T to come to a stop, how long does it take for wheel B to come to a stop?

My work: p=Ft, so m(wf-wi)=uFt, so t=(m(wf-wi)/umg)= (mwi)/(umg)=TA, so since B=2w then the time for B would be 2TA.

(b) Find an expression for T in terms of teh variables specified above.

My work: T=mwi/umg, so T=wi/ug

(c) If wheel A rotates through an angle @ before coming to rest, through what angle does wheel B rotate before coming to rest?

My work: wf^2-wi^2=2a@, so @=(wf^2-wi^2)/(2a) so @=wi^2/2a...So the @B would be 2wi^2/2a, so @B is 4@A. (@ is angle and a is alpha)

(d) Find an expression for @ in terms of teh variables specified above.

My work: @= (wi^2/2a) = (wi^2/2(Ffric/m)) = (wi^2/2(uF/m)) = (wi^2/2(umg/m)) = (wi^2/2ug). So @= (wi^2)/(2ug)

(e) If you doubled the value of uk, how would that affect the time required to stop wheel A?

My work: Doubling the value of uk doubles the friction, which would reduce the time to stop wheel A by 1/2. Double uk would cause 1/2TA.

Thank you for reading through this!