# How much sand is needed to slow the rotation of a disk?

• sskc248
In summary, a disk with a radius of 40 cm and a moment of inertia of 0.015 kg m^2 is rotating at 3 rev/s. Sand falls on the disk at a distance of 20 cm from the axis, forming a 20 cm radius sand ring. To slow the speed of revolution to 2 rev/s, we can use the law of conservation of angular momentum. This involves calculating the angular momentum of the disk, rather than its mass.
sskc248

## Homework Statement

a disk of radius 40 cm is rotating about an axis through its centre. the moment the inertia of the disk is 0.015 kg m^2 and it is turning at 3 rev/s. sand falls on the disk at a distance of 20 cm from the axis and builds a 20 cm radius sand ring on the disc. How much sand must fall on the disc to slow the speed of revolution to 2 rev/s? Use the law of conversation of angular momentum

## The Attempt at a Solution

Angular Momentum L=mvr I know the 40 cm
Moment of Inertia I=mr^2 so mass = .375
How do I approach this problem in what way? what do the rev/s have to do with this problem?

No, the moment of inertia of a disk isn't I=mr2. that would be the case if all the mass of the disk was at the radius r. But you don't need to calculate the disk mass. Calculate the angular momentum of the disk.

## 1. What is the rotating disk sand problem?

The rotating disk sand problem is a classic physics problem that involves a disk rotating at a constant speed while sand is poured onto the disk. The problem aims to determine the shape of the sand pile that forms on the disk and the angle at which the pile reaches its maximum height.

## 2. What factors affect the shape and angle of the sand pile?

The shape and angle of the sand pile are affected by the rotation speed of the disk, the mass of the sand, and the coefficient of friction between the sand and the disk. These factors influence the centripetal force acting on the sand particles, causing them to move towards the outer edge of the disk and form the characteristic conical shape.

## 3. How is this problem relevant in real-life applications?

The rotating disk sand problem has practical applications in fields such as geology, agriculture, and material science. For example, it can help researchers understand the formation of sand dunes and the flow of granular materials. It can also be used to study the behavior of agricultural seeds on rotating disks and the movement of particles in industrial processes.

## 4. What are some assumptions made in solving this problem?

Some common assumptions made in solving the rotating disk sand problem include the uniform distribution of sand particles on the disk, the absence of air resistance, and the constant rotation speed of the disk. These assumptions simplify the problem and allow for a more straightforward analysis, but may not always reflect real-world conditions.

## 5. How is this problem solved?

The rotating disk sand problem can be solved using mathematical equations and principles of centrifugal force, centripetal force, and friction. The solution involves finding the equilibrium angle at which the centripetal force equals the weight of the sand pile, and then using this angle to determine the shape and height of the sand pile. Various methods, such as numerical and experimental approaches, can be used to solve the problem.

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