Understanding the Physics of a Cylinder Rolling Down a Slope

In summary, the conversation involves a question about a cylinder rolling down a slope and the physics involved. The conversation includes a free-body diagram and expressions for the acceleration in the x- and y-directions. The person asking for help is unsure about the accuracy of their understanding and asks for clarification on the angular acceleration and the effects of friction.
  • #1
TauMuon
1
0
I would appreciate some help on this question involving a cylinder rolling down a slope; I'm far from comfortable with the physics involved.

Question here:
LjmIRSr.png


This is my free-body diagram of the forces acting on the cylinder:
tUNGtjV.jpg


Expressions for the acceleration in the x- and y-directions in terms of the forces acting on the cylinder:
ihHqL6q.jpg


Now I think the above is okay. The following is where I get a bit lost...

Expression for the angular acceleration:
rVkSqDe.jpg


Acceleration along x (didn't it already ask for this..?) :
Et8k6F9.png


I really have no clue if the above is even remotely correct. I'm very fuzzy on the physics at the moment, so if someone could take the time to explain it to me I would be immensely grateful.

Thanks!
 
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  • #2
RE diagram: it's a bit strange that ##m\vec g\cos\theta## is pointing upwards. After all, the vectors ##m \vec g\cos\theta## and ##m \vec g\sin\theta## should add up to ##m\vec g##

An unexplained ( :) ) ##\mu## pops up in the diagram.

If I take the diagram seriously, the cylinder should take off from the ramp in the vertical y-direction: forces don't add up to 0 (see first comment re diagram)

so much for a) and b).

c) there's ##\mu## again. For the friction force we usually write ##|\vec F_{fric, max}| = \mu |\vec F_N|## where ##\vec F_N## is the normal force. Hence my "confusion": the friction force let's the thing rotate, but perhaps the maximum friction force is more than is needed to satisfy the no-slip condition... So you want to wonder about this non-slipping and what it means for ##\alpha## and thereby for the friction force..
 

1. What is the formula for calculating the speed of a cylinder rolling down a slope?

The formula for calculating the speed of a cylinder rolling down a slope is v = √(2gh), where v is the speed, g is the acceleration due to gravity, and h is the height of the slope.

2. How does the mass of the cylinder affect its speed while rolling down a slope?

The mass of the cylinder does not affect its speed while rolling down a slope. This is because the formula for calculating speed (v = √(2gh)) does not include the mass of the object.

3. What is the role of friction in the movement of a cylinder rolling down a slope?

Friction plays a significant role in the movement of a cylinder rolling down a slope. It acts in the opposite direction of the motion, slowing down the cylinder's speed. Without friction, the cylinder would continue to roll at a constant speed down the slope.

4. How does the angle of the slope affect the speed of a cylinder rolling down it?

The steeper the slope, the faster the cylinder will roll down it. This is because the height (h) in the speed formula (v = √(2gh)) increases with a steeper slope, resulting in a higher speed.

5. What other factors can affect the speed of a cylinder rolling down a slope?

Other factors that can affect the speed of a cylinder rolling down a slope include the shape and size of the cylinder, the surface of the slope (e.g. roughness), and air resistance. These factors can alter the amount of friction acting on the cylinder and ultimately affect its speed.

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