Question

When a solid sphere rolls down a inclined plane , what is percentage of rotational ke?

Answer 1

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Te total kinetic energy (KE) of an object is given by:

KE=12mv2+12Iω2KE=12mv2+12Iω2

where II is the moment of inertia of the object and ωω its angular momentum. For a solid sphere, the moment of inertia is given by:

I=25mr2I=25mr2

angular velocity would be derived from its radius and linear velocity:

ω=vrω=vr

so the total equation would be:

KE=12mv2+1225mr2vr2KE=12mv2+1225mr2vr2

=12mv2+210mv2=12mv2+210mv2

To get the percentage attributed to rotational energy, we’d divide the rotational part of the energy by the total energy:

210mv212mv2+210mv2=210mv2710mv2=27