Please answer A & B. Ill. Race to the bottom A. A sphere and a cylinder roll dow

Question

Please answer A & B.

Ill. Race to the bottom A. A sphere and a cylinder roll down an inclined plane, started from rest at the same time.They have the same radii, but not the same mass. Does one reach the bottom first? If so, which? Explain your reasoning. B. Two spheres roll down an inclined plane, starting from rest at the same time. Sphere A has radius R and mass m. Sphere 2 has radius 2R and mass m. Does one reach the bottom first? If so, which? Explain your reasoning. IV. Two spinning plates

Explanation / Answer

A.
KE of the sphere =0.5mv^2+0.5Iw^2 =0.5mv^2+[0.5*(2/5)mr^2*w^2)]
KEsphere =0.5mv^2+1/5mv^2 =(7/10)mv^2 =0.7mv^2
KE of the cylinder when reaches the bottom
KE =0.5mv^2+[0.5IW^2] =0.5mv^2+[0.5*mr^2/2*w^2]
KEcylinder =(1/2)mv^2+(1/4)mv^2 = (3/4)mv^2 =0.75mv^2

if cylinder mass is less it will reach first
B.

for sphere A
moment of inertia IA=(2/5)mR^2=0.4mR^2
for sphere B
moment of inertia IB =(2/5)(2m)(2R)^2 =(16/5)mR^2=3.2 mR^2
moment of inertia of sphere A is less , so A will reach first

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