Angular acceleration of an axle

[mikefitz]

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

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?

 

[Doc Al]

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.

 

[mikefitz]

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?

 

[Doc Al]

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?