Rotational motion down an incline (ring/hoop)

In summary: I am an AI and I am not able to interact with images. Can you please provide a written summary of the conversation?In summary, the conversation revolves around a 24kg metal ring rolling down a 30 degree incline with a height of 3.4m and a diameter of 24cm without slipping. The first question asks for the linear speed of the ring at the bottom of the ramp according to the law of conservation of energy. The second question asks for the linear speed of the ring at the base of the incline if it has a moment of inertia of I=mr^2. The third question asks for the average linear acceleration of the ring down the incline. The conversation also includes attempts at solving the questions
  • #1
floraha
2
0

Homework Statement


A 24kg metal ring with 24cm diameter rolls without slipping down a 30 degree incline from a height of 3.4 m.

1) According to the law of conservation of energy what should be the linear speed of the ring at the bottom of the ramp
2) if the ring has a moment of inertia of I=mr^2 what will its linear speed be at the base of the incline?

3) what is the avg linear acc of this ring down the incline?

Homework Equations

3. The Attempt at a Solution [/B]
For part 1, I got the math down to the square root of 2gh, because I assumed they were just asking for Vfrictionless. I did this through the equation PE=KE(translational) + KE (rotational) from which I got mgh = 1/2mv^2+1/2iw^2 where i=moment of inertia and w=angular velocity. In this case (i) would just be zero, getting me 2gh

For part 2 I did the same thing, except I substituted the moment of inertia in for (i) getting the math down to the square root of gh.

I had the most difficult time with part three. I wasn't sure where to start so I just worked out a(tangental) = r * angular acceleration. My teacher told me the answer is gsin(x) but I have no idea how he got there.
 
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  • #2
floraha said:
rolls without stopping
Are you sure that is the correct wording and it wasn't supposed to say, "rolls without slipping". Additionally, because it says "rolls", that suggests that it is not frictionless. If it was frictionless, it would not rotate at all; it would just slide.

Edit: Sorry I forgot to welcome you to Physics Forums. Welcome!
Edit2: Hmm. I think I can see your position that part 1 maybe is supposed to assume frictionless due to the wording of part 2. However, for part 1 the ring had the same moment of inertia as specified in part 2.
 
  • #3
@TomHart Thank you for replying! You were right about the wording, it was actually "slipping." Also, for part 3 it autocorrected to arc when it should have been acc (as in acceleration).
 
  • #4
floraha said:
what is the avg linear acc of this ring down the incline?
You know the initial speed, the final speed and the distance (which is...?). What equation do you know linking those three to acceleration?
 

Related to Rotational motion down an incline (ring/hoop)

1. What is rotational motion down an incline (ring/hoop)?

Rotational motion down an incline (ring/hoop) refers to the movement of a ring or hoop object as it rolls down an inclined plane. This type of motion combines both rotational and translational motion, where the object rotates as it translates down the incline.

2. What factors affect the rotational motion down an incline (ring/hoop)?

The factors that affect rotational motion down an incline include the mass of the object, the radius of the ring or hoop, the angle of the incline, and the surface on which the object is rolling.

3. How does the angle of the incline affect rotational motion down an incline (ring/hoop)?

The angle of the incline affects the rotational motion down an incline in two ways. First, a steeper incline will result in a faster and more unstable roll due to the increased gravitational force pulling the object down the incline. Second, the angle also affects the moment of inertia of the object, which is a measure of its resistance to rotational motion.

4. How is rotational motion down an incline (ring/hoop) related to potential and kinetic energy?

As the ring or hoop rolls down the incline, it converts its potential energy into kinetic energy. The higher the incline, the more potential energy the object has, and the faster it will roll down the incline, resulting in a higher kinetic energy. At the bottom of the incline, all of the potential energy is converted into kinetic energy, and the object will continue to roll until it reaches a flat surface.

5. How does the shape of the object affect its rotational motion down an incline (ring/hoop)?

The shape of the object affects its rotational motion down an incline in several ways. A ring or hoop has a lower moment of inertia compared to a solid cylinder or sphere, making it easier to roll down an incline. Additionally, the shape can also affect the contact area between the object and the incline, which can impact the frictional forces and the stability of the roll.

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