How Fast Does a Cylinder Roll Down an Inclined Plane?

[irony416]

Homework Statement

Problem:

A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15 degrees, and rolls to the bottom without slipping. (I = 0.5MR^2). The upper end of the ramp is 1.2 m higher than the lower end. Find the lindear speed of the cylinder when it reaches the bottom of the ramp.

Homework Equations

Equations:
I = 0.5MR^2 = 0.6

The Attempt at a Solution

Do I use angular momentum here? Really have no idea. Thanks.

 

[Cyosis]

Use conservation of energy. What is the kinetic energy of a rigid body that both translates and rotates?

 

[nlightner]

Yes, you can use angular momentum to solve this problem. Since the cylinder is rolling without slipping, the linear speed can be related to the angular speed by the formula v = ωR, where v is the linear speed, ω is the angular speed, and R is the radius of the cylinder.

To solve for the angular speed, you can use the conservation of energy principle. The initial energy of the cylinder at the top of the ramp is purely potential energy, given by mgh, where m is the mass of the cylinder, g is the acceleration due to gravity, and h is the height of the ramp. At the bottom of the ramp, the energy is a combination of potential and kinetic energy, given by mgh + 0.5Iω^2, where I is the moment of inertia of the cylinder.

Setting these two energies equal to each other and solving for ω, you can then plug in the value of ω into the formula v = ωR to find the linear speed of the cylinder at the bottom of the ramp.

Hope this helps!