Rolling Disk Inertia: Comparing Friction and Slip on Inclines

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In summary, two identical disks with rotational inertia I (= 1/2 MR2) are rolled without slipping across a horizontal floor and up inclines. Disk A rolls up its incline without slipping, while disk B rolls up a frictionless incline. Both inclines are identical. Disk A reaches a height of 12 cm above the floor before rolling down again, while disk B reaches a height above the floor of unknown value. The problem can be solved by finding the ratios of translational and rotational energies and plugging them into the formulas for total and translational energies.
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ctv1337
Two identical disks, with rotational inertia I (= 1/2 MR2), roll without slipping across a horizontal floor and then up inclines. Disk A rolls up its incline without slipping. On the other hand, disk B rolls up a frictionless incline. Otherwise the inclines are identical. Disk A reaches a height 12 cm above the floor before rolling down again. Disk B reaches a height above the floor of?
I've tried a couple of things but i don't think I'm going in the correct direction...can anyone help me?
 
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You can readily see

that the disc on the frictionless incline can't convert it's rotational energy into potential energy, whereas the disc on the frictional incline can covert both its translational and rotational energy into potential energy. Solving the problem is just a matter of finding the ratios of translational and rotational energies and plugging them into the formulas for total and translational only.
 

What is the concept of rolling disk inertia?

The concept of rolling disk inertia is based on the principle of inertia, which states that an object at rest will remain at rest and an object in motion will continue to move at a constant velocity, unless acted upon by an external force. In the case of a rolling disk, the inertia refers to its resistance to changes in its rotational motion.

What is the relationship between friction and slip on inclines?

The relationship between friction and slip on inclines is that they both affect the rotational motion of a rolling disk. Friction, which is the force that resists the motion between two surfaces in contact, can either help or hinder the rolling motion of a disk on an incline. Slip, on the other hand, occurs when the friction force is not strong enough to prevent the disk from sliding down the incline instead of rolling.

How does the angle of the incline affect the rolling disk inertia?

The angle of the incline has a direct impact on the rolling disk inertia. As the incline becomes steeper, the disk experiences more resistance to its rotational motion due to an increase in the component of gravity pulling the disk down the incline. This means that the disk will have a higher inertia and require more force to maintain its rolling motion.

What factors can affect the amount of friction and slip on an incline?

The amount of friction and slip on an incline can be affected by various factors such as the surface material of the incline and the disk, the weight and shape of the disk, and the angle of the incline. The presence of any external forces, such as air resistance or additional weight on the disk, can also impact the friction and slip on the incline.

How can the concept of rolling disk inertia be applied in real-life situations?

The concept of rolling disk inertia can be applied in various real-life situations, such as in the design of vehicles with wheels, the development of sports equipment like roller skates, and the study of the movement of celestial bodies. Understanding the principles of rolling disk inertia can also help in improving the efficiency and stability of machines that involve rotational motion.

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