Rolling motion of a rigid body

In summary, to find the distance the ring goes up the inclined plane, use conservation of energy by calculating the total energy at the point where the ring is 2.0m up the plane, and equating it to the potential energy at the highest point on the plane. The difference between the inner and outer radius should be taken into account when calculating the moment of inertia. Then, use trigonometry and resolving to find the distance up the plane.
  • #1
lunarskull
28
0
A ring of mass 2.4kg, inner radius 6c.0cm, and outer radius 8.0cm is rolling (without slipping) up an inclined plane that makes an angle of theta=36.9 with the horizontal. At the moment the ring is x=2.0 m up the plane its speed is 2.8 m/s. the ring continues up the plane for some additonal distance and then rolls abck down. Assuming that the plane is long enough so that the ring does not roll off the top end, how far up the plane does it go?

help by one of you good samaritans would be greatly appreciated.

so far, I've gotten :

I=.5MR1^2+.5MR2^2
I=.5(2.4)(.06^2)+.5(2.4)(.08)^2
I= .012 kg M^2

what do i do next? i am unaware of how to find distance and incorporate theta into this problem
 
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  • #2
You need to use conservation of energy.
 
  • #3
how?

Hootenanny said:
You need to use conservation of energy.
how do you incorporate the numbers into conservation of energy?
 
  • #4
Assuming x is horizontal displacement you know that at this point the ring is traveling at 2.8m/s. From this you can work out the linear kinetic energy and the rotational kinetic energy. Also if you resolve you can work out the vertical height of the ring and from this you can calculate the potential energy. This will give you the total amount of energy is the system, which must remain constant. When the ring comes to rest (i.e. at its highest point on the plain) you know that there will be no rotational or linear kinetic energy. Therefore, all the energy must be converted into gravitational potential. This will give you a vertical height. Using trig.and resolving you can then calculate the distance up the inclined plane.
 
  • #5
dude the inner radius is 0.06m and outer is 0.08m. you should subtract the value of MIdisk you get for 0.08m from the one you get for 0.06m. Why did you add the two up. It's not making any sense. After you do it you can solve the problem easily by using conservation of energy.
 

1. What is rolling motion of a rigid body?

Rolling motion of a rigid body refers to the movement of a solid object in which it rotates and translates simultaneously. This type of motion is commonly seen in objects such as wheels, balls, and cylinders.

2. How is rolling motion different from other types of motion?

Unlike sliding or spinning motion, rolling motion involves both rotation and translation of an object. This means that the object is in contact with a surface and is able to move forward while also rotating around its axis.

3. What factors affect the rolling motion of a rigid body?

The rolling motion of a rigid body is affected by several factors, including the shape and size of the object, the surface it is rolling on, and the external forces acting on the object.

4. Can rolling motion be described using equations?

Yes, rolling motion can be described using equations such as the rotational kinematic equations and the parallel axis theorem. These equations can be used to calculate the speed, acceleration, and other parameters of a rolling object.

5. What are some real-life examples of rolling motion?

Examples of rolling motion in everyday life include a car moving on its wheels, a ball rolling down a hill, and a rolling pin used in baking. This type of motion is also commonly seen in sports, such as bowling or golf.

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