Question 117 (Unit 7) The moment of inertia of a thin-walled hollow sphere about

Question

Question 117 (Unit 7) The moment of inertia of a thin-walled hollow sphere about any central R2 where M is the mass of the sphere and R is its radius. When such a sphere rolls own an inclined plane, what is the ratio Etrans/ Erot of its translational to its rotational kinetie energy? Question 118 (Unit 7) The moment of inertia of a uniform solid sphere about any central axis is I MR2 where M is the mass of the sphere and R is its radius. When such a sphere rolls down an inclined plane, what is the ratio Erot/ Errans of its rotational to its translational kinetic energy?

Explanation / Answer

Rotational kinetic energy is given by:

KErot = I*w^2/2

translational kinetic energy is given by:

KEtrans = M*V^2/2

For hollow sphere

I = 2*M*R^2/3

w = V/R

KErot = [(2*M*R^2/3)*(V/R)^2]/2

KErot = M*V^2/3

So,

Etrans/Erot = (M*V^2/2)/(M*V^2/3)

Etrans/Erot = 3/2

118.

For solid sphere

I = 2*M*R^2/5

KErot = [(2*M*R^2/5)*(V/R)^2]/2

KErot = M*V^2/5

So,

Erot/Etrans = (M*V^2/5)/(M*V^2/2)

Erot/Etrans = 2/5

Please Upvote

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.