How do I properly set up this F.B.D.?

  • Thread starter Thread starter Vitani11
  • Start date Start date
  • Tags Tags
    Set
Click For Summary
SUMMARY

The discussion focuses on analyzing the motion of a uniform solid cylinder rolling down an incline with angle theta, considering both static and kinetic friction coefficients. The key equation derived is mgsin(theta) - μk = ma, which describes the forces acting on the cylinder. It is established that since the cylinder rolls without slipping, only the static friction coefficient (μs) is relevant for the analysis. Participants emphasize the necessity of setting up two equations: one for translational motion and another for rotational motion to accurately determine the acceleration of the center of mass.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with concepts of static and kinetic friction
  • Knowledge of rotational dynamics and moment of inertia
  • Ability to set up and solve systems of equations
NEXT STEPS
  • Study the relationship between static friction and rolling motion in detail
  • Learn how to derive equations for rotational motion using torque
  • Explore the implications of the no-slip condition in rolling objects
  • Investigate the effects of varying incline angles on acceleration
USEFUL FOR

Physics students, educators, and anyone interested in classical mechanics, particularly those studying dynamics of rolling objects and frictional forces.

Vitani11
Messages
275
Reaction score
3

Homework Statement


A uniform solid cylinder of wood rolls without slipping down an incline of angle theta. the coefficient of static friction is μs and kinetic friction is μk. Find the acceleration of the center of mass of the cylinder.

Homework Equations


mgsin(theta)-μk = ma

The Attempt at a Solution


My question is really how to reconcile with the static friction coefficient. Should this be included in my FBD and so my equation? Or would I just be using the μk and not the μs? If μs is to be included, can you please explain how? Would I have to set up two equations, one to overcome the static friction and the other to characterize the rolling motion with μk, then solve for the acceleration using a two-equation system?
 
Physics news on Phys.org
You are told that the cylinder rolls without slipping, thus the only friction involved is static friction. (Hint: Write two equations: one for rotation, one for translation.)
 
  • Like
Likes   Reactions: Vitani11

Similar threads

Replies
61
Views
4K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
2
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 12 ·
Replies
12
Views
4K
Replies
7
Views
3K
  • · Replies 10 ·
Replies
10
Views
6K
  • · Replies 4 ·
Replies
4
Views
8K
Replies
13
Views
4K