Question

James is completely frustrated by the squirrel trying to chew through his roof. In an effort to drive the squirrel away, his son climbs on the roof to chase it off. While doing so, he unwittingly dislodges a small stone (approximate as a solid cylinder) of mass 3.0 kg and radius 0.20 m that starts from rest at the top of the roof, inclined 30°, and rolls to the bottom without slipping. (For a cylinder I = 0.5MR²) The upper end of the roof is 4.5 m higher than the lower end. Find the linear speed of the cylinder when it reaches the edge of the roof. (Note: I = 0.5MR²)

Answer 1

Here, the change in potential energy will be the sum of the translational kinetic energy and rotational kinetic energy at the bottom. Because of this, we will not need the angle of inclination of the roof, nor will we need the values of radius or mass.

Here, and

Putting these in, we get

Putting in our numeric values, we get