Stopping a rotating disk with an axe

In summary, the problem involves a rotating grindstone with a diameter of 0.480m and a mass of 50.0kg. The grindstone is initially rotating at a rate of 820rev/min and is brought to rest in 8.00s when an ax is pressed against its rim with a normal force of 190N. The goal is to find the coefficient of friction between the ax and the grindstone. The equation of motion for angular velocity, along with the moment of inertia being 1/2MR^2, can be used to solve the problem. Assistance from Galileo was helpful in solving the problem.
  • #1
jaymode
26
0
My problem:
A grindstone in the shape of a solid disk with diameter=0.480m and a mass of m=50.0kg is rotating at omega = 820rev/min. You press an ax against the rim with a normal force of F=190N View Figure , and the grindstone comes to rest in 8.00s.

I need to find the coefficient of friction between the ax and the grindstone.

well the stuff i have some far is that the moment of Inertia is 1/2MR^2. That is really all that I have I just need a hint or something on how to proceed...if someone could help me out.
 
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  • #2
The axe exerts a constant torque [itex]\tau = I\alpha[/itex] on the disk, combine this with the 'equation of motion' for the angular velocity: [itex]\omega(t)=\omega_0+\alpha t[/itex].
 
  • #3
Galileo, thank you. That really helped me figure the problem out.
 

1. How does the rotation of a disk affect the force needed to stop it with an axe?

The rotation of a disk creates angular momentum, which is a measure of how much an object is rotating. This means that the faster the disk is rotating, the more force will be needed to stop it with an axe. The direction of the rotation also matters, as stopping a disk that is rotating clockwise will require a different amount of force than stopping one that is rotating counterclockwise.

2. Is it possible to stop a rotating disk with just one strike of an axe?

It is not likely that a rotating disk can be stopped with just one strike of an axe. The force of the strike would need to be perfectly aligned with the axis of rotation in order to completely stop the disk. Additionally, the force of the strike would need to be greater than the angular momentum of the disk in order to overcome its rotation.

3. How does the thickness and material of the disk affect the force needed to stop it with an axe?

The thickness and material of the disk can have a significant impact on the force needed to stop it with an axe. A thicker disk will have a greater moment of inertia, making it harder to stop. Similarly, a denser material will also have a greater moment of inertia and require more force to stop. Conversely, a thinner disk or a less dense material will require less force to stop.

4. Can stopping a rotating disk with an axe cause any damage to the axe?

Yes, stopping a rotating disk with an axe can cause damage to both the axe and the disk. The force of the strike can cause the blade of the axe to chip or break, and the impact can also cause the disk to crack or shatter. It is important to use caution and proper technique when attempting to stop a rotating disk with an axe.

5. How does the angle of impact affect the force needed to stop a rotating disk with an axe?

The angle of impact, or the angle at which the axe hits the disk, can have a significant impact on the force needed to stop it. Ideally, the axe should strike the disk at a 90-degree angle to the axis of rotation, as this will maximize the force applied to stop the rotation. Striking at an angle less than 90 degrees will require more force, and striking at an angle greater than 90 degrees may cause the axe to glance off the disk instead of stopping it.

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