What Is the Angular Acceleration and Distance Traveled by the Paint Splotch?

In summary, a flywheel with a splotch of paint on it rotates at a rate of 20 rpm and then accelerates to a rate of 70 rpm in 30 seconds. The angular acceleration of the paint splotch is unknown, but can be found by using the equation alpha = (omega2 - omega1)/t. The paint splotch is located 0.10 m from the center of the flywheel, and its distance traveled during the acceleration period can be found using the equation s = (omega1*t)+(1/2*alpha*t^2).
  • #1
RedDanger
11
0

Homework Statement


A flywheel rotates at a rate of 20 rpm. A motor provides a constant angular
acceleration so that 30 s later it turns at a rate of 70 rpm. There’s a tiny splotch of paint on the
flywheel, located 0.10 m from its center. During the acceleration period, what is the angular
acceleration of the splotch of paint in rad/s2, and how far does the splotch of paint travel?


Homework Equations


C = 2pi*r ?


The Attempt at a Solution


I have no idea how to approach this problem, as I missed this day in class and my text isn't very helpful. Even worse, my professor doesn't have any office hours this week! :[
 
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  • #2
RedDanger said:

The Attempt at a Solution


I have no idea how to approach this problem, as I missed this day in class and my text isn't very helpful. Even worse, my professor doesn't have any office hours this week! :[

Firstly, read http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html" for the equations (scroll down to Description of equations)

It asks you to get the angular acceleration, so which equation will give you that value given just the angular velocity (which you can get the change in) and time?
 
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  • #3
(revolutions per minute) x ( (2*pi) / (60sec) )= omega in rad/sec

you want to find the change in omega over time, or alpha in rad/sec^2
 

FAQ: What Is the Angular Acceleration and Distance Traveled by the Paint Splotch?

1. How do you calculate the angular acceleration of a paint splotch on a flywheel?

To calculate the angular acceleration of a paint splotch on a flywheel, you will need to know the initial and final angular velocities of the flywheel, as well as the time it took for the flywheel to reach its final velocity. The formula for angular acceleration is (final angular velocity - initial angular velocity) / time.

2. What is the formula for calculating the distance traveled by a paint splotch on a flywheel?

The formula for calculating the distance traveled by a paint splotch on a flywheel is d = r * θ, where d is the distance traveled, r is the radius of the flywheel, and θ is the angular displacement of the paint splotch.

3. How do you convert angular velocity to linear velocity?

To convert angular velocity to linear velocity, you will need to know the radius of the flywheel. The formula is linear velocity = angular velocity * radius.

4. Can you use the same formula to calculate the distance traveled for any size flywheel?

Yes, the formula for calculating the distance traveled by a paint splotch on a flywheel (d = r * θ) can be used for any size flywheel as long as you know the radius and angular displacement.

5. How does the mass of the paint splotch affect the calculation of angular acceleration and distance traveled?

The mass of the paint splotch does not affect the calculation of angular acceleration and distance traveled on a flywheel. This is because the formula for angular acceleration and distance traveled only take into account the angular velocity and displacement of the flywheel, not the mass of the object on it.

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