Suppose you have a cylinder with a partially - hollow interior: an inner radius

Question

Suppose you have a cylinder with a partially - hollow interior: an inner radius R1 and outer radius R2. (The solid portion of the object has uniform density.) When rotating about its axis of symmetry . the moment of inertia of this partially - hollow cylinder is: You do NOT need to show your work. Be sure to include correct units aid sig. figs.! Suppose the object rolls without slipping down a 0.95 - m - high ramp. When it gets to the bottom, it has a linear speed of 3.3 m/s. If the object has a mass of 3 - 8 kg and an outer radius R2 = 0.18 m. calculate its inner radius, R1: If you were to release this partially - hollow cylinder right next to a solid cylinder. which one would accelerate down the ramp faster Assume that both of their masses and outer radii are identical. the solid cylinder both would have the same acceleration the partially - hollow cylinder cannot determine from information given

Explanation / Answer

a) conservation ofenergy

Ei = Ef

m g h = 1/2 mv^2 + 1/2 I w^2

w = v/R2 and plug in for I
m g h = 1/2 m v^2 + 0.5*m/2 (R1^2 + R2^2) *(v/R2)^2

9.81*0.95 = 0.5*3.3^2 + 0.5/2*(R1^2 + 0.18^2)*(3.3/0.18)^2

R1=0.117 m

b)a solid cylinder has I = M R^2/2
so less moment of inertia
so it would accelerate faster since easier to spin

so A)

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