Download Rolling wheel on inclined plane

 Example 11.*** – Rolling wheel on inclined plane The rolling wheel shown at right is released from rest. Assume that the coefficient of static friction is high enough that the wheel begins to roll down the plane instead of sliding. Find and  of the wheel just after it is released from rest. Then find the friction force that opposes the motion of the wheel. Solution – Apply Newton’s Second Law to the wheel. FBD Figure 11.*** ‐ Rolling wheel on inclined plane = MAD Sum moments about A to eliminate the friction force. ∑
:
̅ sin
From kinematics Thus ̅ sin
sin
̅
sin
̅
Now let’s look at the friction force on the wheel. ∑
: sin
̅
11‐1 sin
1
̅
Note that if this force were greater than sN , the wheel would begin to slide down the ramp instead of rolling. Or, seen another way, sin
1
̅
cos
tan
1
̅
Note that if ̅ is high, it will make the second term small, and it will require a higher to prevent the wheel from rolling. On the other hand if ̅ is small, it doesn’t take much of a friction coefficient to prevent the wheel from rolling. Also note: If we take moments about O, only Ff has a moment about O. ∑
̅ :
̅
That is, the greater ̅ , the smaller . You could also look at as the force that gets the wheel spinning. As an aside, note that even on a flat surface, if the wheel is moving at a constant velocity FBD = MAD ∑
:
0 Thus, when a wheel is rolling at a constant speed, there is no friction force. 11‐2