Angular acceleration of an axle

In summary, a disk with a radial line painted on it is mounted on an axle and undergoes constant angular acceleration. After accelerating for 3.1 seconds, the reference line has moved to 130 degrees. The angular acceleration is 0.79911 rad/s^2. To find the angular speed after one complete revolution, we can use the kinematic relationship v = u + at, where v is the final velocity (unknown), u is the initial velocity (zero), a is the constant angular acceleration, and t is the time taken for one complete revolution (unknown). We can also use the relationship s = ut + (1/2)at^2, where s is the total angle traveled (360 degrees) and
  • #1
mikefitz
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A disk with a radial line painted on it is mounted on an axle perpendicular to it and running through its center. It is initially at rest, with the line at theta 0 = -90°. The disk then undergoes constant angular acceleration. After accelerating for 3.1 s, the reference line has been moved part way around the circle (in a counterclockwise direction) to theta f = 130°.

Given this information, what is the angular speed of the disk after it has traveled one complete revolution (when it returns to its original position at -90°)?


http://img175.imageshack.us/img175/6909/picwe9.gif [Broken]

here is my work:

360-130=230 degrees.

130(pi/180)=2.26 radians
230(pi/180)=4.014 radians

theta=Wot + at^2 /2

4.014 = a (9.61)/2
9.61a = 8.09

a1=.84 radians

2.26/3.1 = .73 rad/s

a2=.73 radians

.84 + .73 = 1.57 rad/s

I found the acceleration of the first 130 degrees; the acceleration of the last 230 degrees, added them, but my answer is wrong. any idea why?
 
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  • #2
mikefitz said:
here is my work:

360-130=230 degrees.
The disk moves from -90 degrees to 130 degrees: 130 - (-90) = 220 degrees in the time given. Find the angular acceleration using that data.
 
  • #3
I've calculated 220 (pi/180) = 3.8397 rad/s

3.8397 rad = (a(9.61))/2
a = .79911 rad/s

So I have calculated the constant acceleration; how do I find the speed after one revolution?
 
  • #4
mikefitz said:
I've calculated 220 (pi/180) = 3.8397 rad/s

3.8397 rad = (a(9.61))/2
a = .79911 rad/s
Good. (But the units are rad/s^2.)

So I have calculated the constant acceleration; how do I find the speed after one revolution?
It's just another kinematics problem. What other kinematic relationships are you familiar with? (One useful one relates velocity and distance--or angular velocity and angle--directly.) What can you determine from the given data?
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity. It measures how quickly the rotational speed of an object changes over time.

2. How is angular acceleration different from linear acceleration?

Angular acceleration refers to the change in rotational speed, while linear acceleration refers to the change in linear velocity. In other words, angular acceleration measures how quickly an object is spinning, while linear acceleration measures how quickly an object is moving in a straight line.

3. How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The unit of measurement for angular acceleration is radians per second squared (rad/s²).

4. What is the relationship between angular acceleration and torque?

Angular acceleration is directly proportional to the torque applied to an object. This means that the greater the torque, the greater the angular acceleration will be.

5. What factors can affect the angular acceleration of an axle?

The angular acceleration of an axle can be affected by variables such as the mass of the object attached to the axle, the distance of the mass from the center of rotation, and the torque applied to the axle. Friction and air resistance can also play a role in the overall angular acceleration of an axle.

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