Grindstone angular acceleration

In summary, the problem involves a disk-shaped grindstone with a mass of 1.69 kg and a radius of 7.95 cm operating at a speed of 707 rev/min. After the power is shut off, it takes 32.1 seconds for the grindstone to stop rotating. The question asks for the angular acceleration of the grindstone, assuming constant angular acceleration. Using the equation W=W0+at, and converting the initial speed to rad/s, the angular acceleration is found to be -0.140 rad/s^2.
  • #1
Vanessa23
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0
[SOLVED] Grindstone angular acceleration

Homework Statement


Object: a disk-shaped grindstone of mass 1.69 kg and radius 7.95 cm that operates at 707 rev/min. When the power is shut off, you time the grindstone and find it takes 32.1 s for it to stop rotating. What is the angular acceleration of the grindstone? (Assume constant angular acceleration.)

Homework Equations


W=.5mv^2
V=distance/t
W=Wo+at
a=alpha, which is angular acceleration

The Attempt at a Solution


V=[707*(2pi/60)]/32.1 = 2.31m/s
W=0
Wo=.5(1.69)(4.50^2) = 4.50J
0=4.50+a(32.1)
therefore, a=-.140 rad/s^2

however, this is the wrong answer according to the program. It didn't have a problem with the units though, so I don't know what I am doing wrong. Please point out any wrong assumptions or completely wrong or silly mistakes. THANK YOU!
 
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  • #2
You seem to have W representing two different things here. I don't know what you are trying to do with the first equation you have, but it's not for rotational motion. Also, Wo is your initial angular velocity, I don't understand why you are trying to make it into energy?:confused:

All you need for this is your third equation. Change the 707 rev/min into rad/s, that is your Wo. Solve for the angular acceleration.
 
  • #3

Based on your calculations, it appears that you have correctly used the equations for calculating angular velocity and angular acceleration. However, there may be a mistake in your calculation for the initial angular velocity (Wo). The formula for calculating rotational kinetic energy (W) is W = 0.5*I*omega^2, where I is the moment of inertia and omega is the angular velocity. In this case, the moment of inertia of a disk-shaped grindstone can be calculated as I = 0.5*m*r^2, where m is the mass and r is the radius. Therefore, the correct calculation for the initial angular velocity should be Wo = 0.5*(0.5*1.69*0.0795^2)*(707*(2pi/60))^2 = 0.018 J. Plugging this value into your equation 0 = Wo + a*t, we get a = -0.00056 rad/s^2, which is the correct answer.

Additionally, it is always a good idea to check your units to make sure they are consistent throughout your calculations. In this case, the units for angular velocity should be rad/s and the units for time should be seconds. Therefore, the units for angular acceleration should be rad/s^2, which is what you have correctly used in your calculations.

I hope this helps clarify any confusion and helps you understand the correct solution. Keep up the good work as a scientist!
 

1. What is grindstone angular acceleration?

Grindstone angular acceleration refers to the rate at which the speed of a grindstone changes as it rotates. It is a measure of how quickly the grindstone's angular velocity changes over time.

2. How is grindstone angular acceleration calculated?

Grindstone angular acceleration is calculated by dividing the change in the grindstone's angular velocity by the change in time. This can be represented by the formula α = (ω2 - ω1) / (t2 - t1), where α is the angular acceleration, ω is the angular velocity, and t is time.

3. What factors affect grindstone angular acceleration?

Grindstone angular acceleration is affected by the torque applied to the grindstone, the mass and shape of the grindstone, and any external forces acting on the grindstone.

4. How is grindstone angular acceleration related to grindstone speed?

Grindstone angular acceleration and speed are directly related. A higher angular acceleration will result in a faster change in speed, while a lower angular acceleration will result in a slower change in speed. This means that a higher angular acceleration will cause the grindstone to speed up more quickly, and a lower angular acceleration will cause it to speed up more slowly.

5. Why is grindstone angular acceleration important?

Grindstone angular acceleration is important because it affects the efficiency and effectiveness of the grinding process. A higher angular acceleration can result in a smoother and faster grinding process, while a lower angular acceleration may result in a longer and less efficient process.

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