Calculating Acceleration of a Cylinder on an Incline

In summary, the conversation is about a difficult exam question involving a solid cylinder rolling down an inclined roof and the acceleration of the cylinder. The acceleration is shown to be a = (2gsinθ)/3, and the question is worth 6 marks. The conversation also includes a helpful link for further information.
  • #1
muppet
608
1
The first part to an exam question I had to sit at the end of last year. It defeated me then, and I still can't do it now, which worries me more than a little!

Homework Statement


A solid cylinder of radius 10 cm and mass 12 kg starts from rest and rolls
without slipping a distance L = 6:0 m down a roof that is inclined at an
angle [tex]\theta[/tex] = 30[tex]\circ[/tex]
Show that the acceleration of the cylinder is given by
a= [tex]\frac{2gsin\theta}{3}[/tex]


Homework Equations


The acceleration of a block down a frictionless incline is just gsin [tex]\theta[/tex]
The moment of inertia of a solid cylinder of mass m and radius r
is given by I = [tex]\frac{1}{2}[/tex]mr[tex]^{2}[/tex]


The Attempt at a Solution


As 2, but I really don't know where the factor of two thirds comes from. The question was worth 6 marks.
 
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  • #3
Fantastic. Thanks :smile:
 

1. What is the purpose of studying a cylinder on an incline?

The purpose of studying a cylinder on an incline is to understand the motion and behavior of objects on an inclined surface, which is a common scenario in real-world situations. This study can also help in predicting the path and speed of the object, as well as the forces acting upon it.

2. What factors affect the motion of a cylinder on an incline?

The motion of a cylinder on an incline is affected by several factors, including the angle of the incline, the mass and shape of the cylinder, the coefficient of friction between the cylinder and the surface, and the presence of any external forces such as gravity or applied forces.

3. How does the angle of the incline affect the motion of a cylinder?

The angle of the incline plays a significant role in determining the motion of a cylinder. A steeper incline will result in a faster and more accelerated motion, while a gentler incline will result in a slower and more controlled motion. This is because the angle affects the component of gravity acting along the incline, which in turn affects the net force and acceleration of the cylinder.

4. What is the relationship between the coefficient of friction and the motion of a cylinder on an incline?

The coefficient of friction between the cylinder and the incline surface determines the amount of resistance to motion. A higher coefficient of friction will result in a slower motion, while a lower coefficient of friction will result in a faster motion. If the coefficient of friction is zero, the cylinder will slide down the incline without any resistance.

5. How can we calculate the speed and acceleration of a cylinder on an incline?

The speed and acceleration of a cylinder on an incline can be calculated using Newton's laws of motion, along with the known forces acting upon the cylinder, such as gravity and friction. The angle of the incline, mass of the cylinder, and coefficient of friction are also important factors in these calculations. Additionally, using mathematical equations such as the equations of motion and the work-energy theorem can help determine the speed and acceleration of the cylinder.

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