A solid disk, a hoop, a solid sphere, and a hollow sphere roll downa hill. Each

Question

A solid disk, a hoop, a solid sphere, and a hollow sphere roll downa hill. Each object is 15 kg and has a radius of 2.3 meters. Theelevation of the hill is 100 meters and all the objects rollwithout friction. What is the final velocity of the objects uponreaching the bottom of the hill? What is the linear kinetic energy,rotational kinetic energy, and the total kinetic energy of theobjects upon reaching the bottom of the hill?
Solid Disk 1 m/sec

Solid Disk rotaional KE 2J

Solid Disk linear KE 3 J

Solid Disk total KE 4 J

Hoop 5 m/sec

Hoop rotaional KE 6 J

Hoop linear KE 7 J

Hoop total KE 8 J

Solid Sphere 9 m/sec

Solid Sphere rotaional KE 10 J

Solid Sphere linear KE 11 J

Solid Sphere total KE 12J

Hollow Sphere 13 m/sec

Hollow Sphere rotaional KE 14 J

Hollow Sphere linear KE 15 J

Hollow Sphere total KE 16 J

Explanation / Answer

This is a pretty simple question with just a few varifications. Look in the book, I think page 253 for the table of inertias forcertain objects. then set conservation of energy. i guess assume start from rest (PE + Rotational Kinetic Energy+KE)intial=(PE + RKE+KE)final (MGH + 0 + 0= 0 + 1/2*I*w2+ 1/2*M*v2 solve for V helpful conversions: W=Rv                       I= depending on object and radius

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