Torque problem involving rolling disk stopped by a force

[xregina12]

A potter has a stone disk of radius 0.483 m and mass 101 kg rotating at 71.9 rev/min. The potter stops the wheel in 6.54 seconds by applying a wet towel against the rim with a radially inward force of 103 N. Find the effective coefficient of kinetic friction between the whell and the wet towel.
my work
angular velocity= 71.9 x 2 x pi /60seconds=7.53
alpha =7.53 / 6.54=1.15
Torque=alpha x I = 1.15 x (101) x (.483^2) =27.13 N-M
27.13 = torque = F r sin 90
F =27.13/ (0.483)
F =56.17 Newtons = Frictional force
56.2 = u Fn
u=56.2 / (103) ----> 103 is given as the radially inward force, Fn
u=.545

why is this wrong? does anyone know why? thanks

 

[tiny-tim]

Hi xregina12!

(have an alpha: α and an omega: ω and a mu: µ and a squared: ² )

A potter has a stone disk of radius 0.483 m and mass 101 kg
…
Torque=alpha x I = 1.15 x (101) x (.483^2)

I = mr²/2 …

see http://en.wikipedia.org/wiki/List_of_moments_of_inertia

 

[thomate1]

There are a few potential issues with your work that may have led to an incorrect answer. Here are a few things to consider:

1. Make sure you are using the correct units throughout your calculations. In this problem, the radius is given in meters, but you used centimeters in your calculation of torque. This may have led to an incorrect value for torque and therefore an incorrect value for frictional force.

2. When calculating torque, it is important to use the correct value for the moment of inertia (I). In this problem, the disk is rotating about its center, so you should use the formula for a solid disk rotating about its center, which is I = 1/2 * m * r^2. You used the formula for a solid disk rotating about its edge, which would be correct if the disk was rotating about its edge, but not in this case.

3. Your calculation for the frictional force (F) is incorrect. The torque equation you used assumes that the force is acting at a right angle to the radius of the disk, but in this problem, the force is acting at an angle of 90 degrees to the radius. This means that you need to use the formula F = torque / (r * sin(theta)), where theta is the angle between the force and the radius. In this case, theta = 90 degrees, so sin(theta) = 1. Using this formula, you should get a value of F = 27.13 N, which is the same as the torque you calculated.

Overall, it's important to carefully consider the given information and use the correct formulas and units in your calculations. Double-checking your work and making sure it is consistent with the given information can also help catch any potential errors.