A spherical object (with non-uniform density)of mass 30 kg and radius 0.22 m rolls along ahorizontal surface at a constant linear speedwithout slipping. The moment of inertia ofthe object about a diameter is 0.56 M R2.The object’s rotational kinetic energyabout its own center is what fraction of theobject’s total kinetic energy?

Question
Asked Nov 19, 2019
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A spherical object (with non-uniform density)
of mass 30 kg and radius 0.22 m rolls along a
horizontal surface at a constant linear speed
without slipping. The moment of inertia of
the object about a diameter is 0.56 M R2.
The object’s rotational kinetic energy
about its own center is what fraction of the
object’s total kinetic energy?

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Expert Answer

Step 1

Given,

Mass of object, M 30 Kg
Radius of object, R 0.22 m
Moment of Inertia,/ =0.56MR
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Mass of object, M 30 Kg Radius of object, R 0.22 m Moment of Inertia,/ =0.56MR

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Step 2

If the ratio of rotational kinetic energy to total kinetic energy for a sph...

Rotational Kinctic Encrgy
Total Kinetic Encrgy
2
Ia Mv
2
where,velocity (v)-(AngularVelocityx Radius)
vR
oR
I M
2
2
1
I MaR
2
2
If we cancel a andin numerator and denominator then,
1+MR
Given, 1 0.56MR
0.56MR
0.56MR2 +MR
0.56MR
1.56MR
r 0.36
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Image Transcriptionclose

Rotational Kinctic Encrgy Total Kinetic Encrgy 2 Ia Mv 2 where,velocity (v)-(AngularVelocityx Radius) vR oR I M 2 2 1 I MaR 2 2 If we cancel a andin numerator and denominator then, 1+MR Given, 1 0.56MR 0.56MR 0.56MR2 +MR 0.56MR 1.56MR r 0.36

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