Acceleration and Friction of a Rolling Cylinder

AI Thread Summary
To find the acceleration of a lawn roller modeled as a thin-walled hollow cylinder, the relationship between friction, force, and acceleration must be established. The equations indicate that the friction force is equal to Ma, where M is the mass and a is the acceleration. However, confusion arises when substituting this back into the force equation, leading to the equation F - ma = ma. The user seeks clarification on the correct approach to solve for acceleration and friction without encountering contradictions. Understanding the relationship between linear and angular acceleration is crucial for resolving the problem correctly.
hm8
Messages
16
Reaction score
0

Homework Statement


A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle.

a)If it rolls without slipping, find the acceleration.

b)If it rolls without slipping, find the friction force.

Homework Equations


I_{Hollow Cylinder} = MR^{2}

\sum \tau = f_{friction}R = I\alpha = MR^{2}\alpha

\sum F = F - f_{friction} = F = Ma

The Attempt at a Solution


I'm really not sure...it seems like I have too many unknowns (R, a, alpha, friction)
 
Physics news on Phys.org
Ok, so I just remembered that because its not slipping, I can change \alpha to \frac{a}{r}

so I get f_{friction}R = MR^{2}*\frac{a}{R}

which cancels down to f_{friction} = Ma

But when I plug that back into the other equation I just get F - ma = ma...

where did I go wrong?
 
Any help, guys?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Wooden sphere rolling on a double metal track
2
Replies
97
Views
5K
Cylinder Rolling Down an Incline Without Slipping
Replies
7
Views
4K
Rod with Current on Rails in Magnetic Field
Replies
12
Views
1K
Why is the direction of kinetic/static friction up a ramp?
Replies
7
Views
1K
Rolling without slipping problem
Replies
42
Views
3K
Analyzing acceleration of block on a ramp connected to a pulley
Replies
15
Views
1K
Stretched spring attached to the center of a pure rolling disk
Replies
11
Views
1K
Cylinder rolling on a moving board
Replies
16
Views
3K
Rotating spool on table with friction
Replies
12
Views
4K
Friction Required for Billiard Ball to Roll without Slipping
2
Replies
60
Views
3K

Hot Threads

Recent Insights

Back
Top