Question

A solid cylinder of mass M and radius R starts from rest and rolls without slipping down an inclined plane of lenght L. Find the speed of its center of mass when the cylinder reaches the bottom

Answer 1

By conservation of energy

2

1

mν

2

+

2

1

Iω

2

=Mgh

but V=Rω ; I=

2

1

MR

2

⇒

2

1

mν

2

+

2

1

(

2

1

mν

2

)=Mgh

4

3

mν

2

=Mgh

ν=

3

4gh