Question

A solid cylinder of radius 10 cm and mass 12 kg starts from rest and rolls without slipping a distance L = 6.0 m down a roof that is inclined at angle  = 30o . a. What is the linear speed and the angular speed of the cylinder about its center as it leaves the roof? b. The roof’s edge is at height H = 5.0 m. How far horizontally from the roof’s edge does the cylinder hit the level ground?

Answer 1

a) Let the total kinetic energy of the cylinder at the point where the cylinder leaves the roof is K_E.

Let the angular speedof the cylinder is .

Let the linear speed of the cylinder is v.

  

  

     

[Here h is the height of the starting point of the motion of the cylinder and the point where the cylinder leaves the roof]

  

  

  

  

  

b) The linear speed of the cylinder

  

Now ,

  

  

[Time is always positive]

  

Let the horizontal component of the velocity v at the point where cylinder leaves the roof is v_x.

  

Horizontal distance from the roof edge where the cylinder hit the ground is

  

The cylinder hit the ground far from the ground level edge of the roof .