# Is My Calculation of a Rolling Steel Hoop's Acceleration Correct?

• dyn
In summary, the conversation discusses the relationship between the acceleration of the center of mass and angular acceleration in the case of rolling without slipping. The speaker also addresses the role of friction in determining the correct answer for the acceleration of the hoop.
dyn
Homework Statement
Hi.
Question concerns a steel hoop of mass 5kg rolling without slipping down a ramp inclined at 30 degrees to the horizontal. What is it's acceleration ?
Relevant Equations
F=ma and resolving component of weight parallel to ramp
I already have the answer but it doesn't make sense. For starters I think the question is worded badly. I think there are 2 different accelerations here ? The acceleration of the centre of mass and the acceleration due to rotation. I think the acceleration due to rotation doesn't affect the acceleration of the centre of mass so I resolved the component of the weight down the ramp which is mgsinθ ; taking g as 10 gives this as 25 and using F=ma gives the acceleration of the COM as 5 m/s^2
Is my reasoning incorrect ?
Thanks

In case of rolling without slipping, there is a relation between the acceleration of the centre of mass, and angular acceleration which reads ##a = R\alpha##. Where ##R## is radius of the hoop. This relation is derived from looking at the point where hoop is touching the ground while rolling. If there is no slipping, that point should be at rest relative to the surface on which the hoop is moving, hence the acceleration that is coming from rotation and translation should cancel at that point.

As for your reasoning, the reason why the hoop is not slipping is because you have friction with the surface it is rolling on, so therefore, you need to add friction into the Newton law for translation, as well as rotation, in order to get the correct answer.

dyn, Delta2 and DaveE

## What is the concept of a steel hoop rolling down a ramp?

The concept of a steel hoop rolling down a ramp is an example of potential energy being converted into kinetic energy. As the hoop is released at the top of the ramp, it has potential energy due to its position and height. As it rolls down the ramp, this potential energy is converted into kinetic energy, which is the energy of motion.

## What factors affect the speed of the steel hoop rolling down the ramp?

The speed of the steel hoop rolling down the ramp is affected by several factors, including the angle of the ramp, the initial height of the hoop, the mass of the hoop, and any external forces acting on the hoop, such as friction. The steeper the ramp, the higher the initial height, and the lower the mass of the hoop, the faster it will roll down the ramp.

## How does the shape of the ramp affect the steel hoop's motion?

The shape of the ramp can greatly affect the steel hoop's motion. A smooth, curved ramp will allow the hoop to roll smoothly and maintain its speed, while a bumpy or rough ramp may slow down the hoop or cause it to veer off course. Additionally, the angle of the ramp can also affect the hoop's motion, with steeper angles resulting in faster speeds.

## What is the relationship between the kinetic energy and potential energy of the steel hoop rolling down the ramp?

The kinetic energy and potential energy of the steel hoop rolling down the ramp are directly related. As the hoop gains speed and kinetic energy, its potential energy decreases. At the bottom of the ramp, all of the potential energy has been converted into kinetic energy, resulting in the hoop's maximum speed.

## How does friction impact the motion of the steel hoop rolling down the ramp?

Friction can have a significant impact on the motion of the steel hoop rolling down the ramp. Friction is a force that acts in the opposite direction of motion and can slow down the hoop as it rolls down the ramp. To minimize the effects of friction, a smooth and well-lubricated ramp should be used, and the hoop should be made of materials that reduce friction, such as plastic or metal.

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