O 11/30/2015 06:00 PM A 72.5/100 11 /29/2015 09:40 PM Gradebook Print d calculat

Question

O 11/30/2015 06:00 PM A 72.5/100 11 /29/2015 09:40 PM Gradebook Print d calculator Periodic Table Question 20 of 29 Map sapling learning A sphere of radius 3.34 cm and a cylinder of radius 7.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the sphere's angular speed to the cylinders angular speed be? Number sph cyl AO Previous ® Give Up & View solution 2 Check Answer Next Exit 8 Hin

Explanation / Answer

Total kinetic energy = 0.5*I*w^2 + 0.5*m*v^2

for sphere, I = 2/5*m*r^2 (I am assuming sphere to be solid)
v = r * w

so,
total kinetic energy of sphere,
Ksphere = 0.5*I*w^2 + 0.5*m*v^2
=0.5*(2/5*m*r^2)*w^2 + 0.5*m*(r*w)^2
=0.5*(2/5*m*(0.0334)^2)*w^2 + 0.5*m*(0.0334*w)^2
= 7.81*m*w^2
  
for cylinder, I = 1/2*m*r^2 (I am assuming cyclinder to be solid)
v = r * w

so,
total kinetic energy of sphere,
Kcylinder = 0.5*I*w^2 + 0.5*m*v^2
=0.5*(1/2*m*r^2)*w^2 + 0.5*m*(r*w)^2
= 0.5*(1/2*m*(0.0797)^2)*w^2 + 0.5*m*0.0797*w)^2
= 1.5*m*w^2

given:
Ksphere = Kcylinder
7.81*m*wsph^2 = 1.5*m*wcyl^2
wsph/wcyl = 0.44

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