2. A thin cylindrical ring starts from rest at a height h, = 95 m. The ring has a radius R = 20 cm and a mass M = 7 kg. Part (a) Write an expression for the ring's initial energy at point 1 if the gravitational potential energy at point 3 is zero. R h, 2 Part (b) If the ring rolls (without slipping) all the way to point 2, what is the ring's energy solutionspile.com

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2. A thin cylindrical ring starts from rest at a height h, = 95 m. The ring has a radius R = 20 cm and a mass M = 7 kg. Part (a) Write an expression for the ring's initial energy at point 1 if the gravitational potential energy at point 3 is zero. R h, 2 Part (b) If the ring rolls (without slipping) all the way to point 2, what is the ring's energy at point 2 in terms of h? and v?? Part (c) Given h? = 35 m, what is the velocity of the ring at point 2 in m/s? 3 Part (d) What is the ring's rotational velocity in rad/s at point 2? Part (e) After passing point 2 the hill becomes frictionless, and the ring's rotational velocity remains constant. What is the linear velocity of the ring at point 3 in m/s?

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2. A thin cylindrical ring starts from rest at a height \\( h_{1}=95 \\mathrm{~m} \\). The ring has a radius \\( R=20 \\mathrm{~cm} \\) and a mass \\( M=7 \\mathrm{~kg} \\). Part (a) Write an expression for the ring's initial energy at point 1 if the gravitational potential energy at point 3 is zero. Part (b) If the ring rolls (without slipping) all the way to point 2 , what is the ring's energy point 2 in terms of \\( h_{2} \\) and \\( v_{2} \\) ? Part (c) Given \\( h_{2}=35 \\mathrm{~m} \\), what is the velocity of the ring at point 2 in \\( \\mathrm{m} / \\mathrm{s} \\) ? Part (d) What is the ring's rotational velocity in \\( \\mathrm{rad} / \\mathrm{s} \\) at point 2? Part (e) After passing point 2 the hill becomes frictionless, and the ring's rotational velocity remains constant. What is the linear velocity of the ring at point 3 in \\( \\mathrm{m} / \\mathrm{s} \\) ?

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