A uniform solid sphere is set rotating about a horizontal axisat an angular spee

Question

A uniform solid sphere is set rotating about a horizontal axisat an angular speed and then is placed on the floor with itscenter of mass at rest. if the coefficient of kinetic friction b/wthe sphere and the floor is k, find the speed of thecenter of mass of the sphere when it begins to roll withoutslipping. I don't understand how to use the coefficient of kineticfriction to find the speed of the center of mass. I tried usingmoment of inertia and that vcm=2r but i'm not getting theright answer of v=2r/7 A uniform solid sphere is set rotating about a horizontal axisat an angular speed and then is placed on the floor with itscenter of mass at rest. if the coefficient of kinetic friction b/wthe sphere and the floor is k, find the speed of thecenter of mass of the sphere when it begins to roll withoutslipping. I don't understand how to use the coefficient of kineticfriction to find the speed of the center of mass. I tried usingmoment of inertia and that vcm=2r but i'm not getting theright answer of v=2r/7

Explanation / Answer

Moment of inertia =2/5Mr2 The torque is provided by frictional force(Ff) =N Initially, the body possesses only rotational energy given by1/2I2 When set on ground, it gains kinetic energy at the expense ofrotational energy. so by conservation of energy:1/2I2=1/2If2+1/2Mv2 Since the body rolls without slipping, we know that v=r or=v/r I2=Iv2/r2+Mv2     I2r2=Iv2+Mv2r2   2/5Mr42=2/5Mr2v2+Mr2v2   2/5Mr42=7/5Mr2v2    2r22=7v2    v2=2/7r22    v=r2/7 I believe it is under-root 2/7, not just 2/7, You don't really needfriction to solve this problem, its just there to remind you thatthe sphere "does" roll and not just stay in one place (sincefriction provides torque for rolling )

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.