a solid sphere with a uniform surface density is rolling over a plane. It\'s rot
ID: 1411266 • Letter: A
Question
a solid sphere with a uniform surface density is rolling over a plane. It's rotational kinetic energy is 80 J. What is the kinetic energy of the linear motion ( translational kinetic energy ) and total kinetic energy? a solid sphere with a uniform surface density is rolling over a plane. It's rotational kinetic energy is 80 J. What is the kinetic energy of the linear motion ( translational kinetic energy ) and total kinetic energy? a solid sphere with a uniform surface density is rolling over a plane. It's rotational kinetic energy is 80 J. What is the kinetic energy of the linear motion ( translational kinetic energy ) and total kinetic energy?Explanation / Answer
Moment of inertia (I) of solid sphere
Is = 2MR^2/5
w = v/R
rotational kinetic energy = KEr
KEr = 0.5*Iw^2
translational kinetic energy = KEt
KEt = 0.5*Mv^2
KEr = 80 J = 0.5*Iw^2
Iw^2 = 160 J
2MR^2*v^2/5R = 160 J
2Mv^2/5 = 160 J
Mv^2 = 400 J
Now,
KEt = 0.5*Mv^2
KEt = 0.5*400 = 200 J
Total KE = KEr + KEt
Total KE = 80 + 200
Total KE = 280 J
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