Angular Motion Question Understanding help ?

[uaeXuae]

Homework Statement

A figure skater completes a double axle (2 complete rotations) in 0.5 seconds. Calculate
the skater’s angular velocity and average angular velocity in a) deg/sec, and b) rad/sec.

If the skater manages to stop spinning in a time of 1.5 seconds,
what was the angular acceleration and average angular acceleration during this period (in deg/s)?

Homework Equations

Average Angular Velocity => w=(Theta2-Theta1)/(t2-t1)
Angular Velocity = theta/time

Average Angular Acceleration => Alfa = (w2-w1)/(t2-t1)
Angular Acceleration => Alfa = (w)/(t)
wf=wi + alfa*(t)

The Attempt at a Solution

Angular Velocity => w=(360*2)/0.5 = 1440 deg/s
1440 * (pi/180) = 23.132 rad/s

Average Angular Velocity => w=(Theta2-Theta1)/(t2-t1)
Average Angular Velocity => w=(360-360)/0.5 = 0 rad/s


Angular Acceleration => Alfa = (w)/(t)
Angular Acceleration => Alfa = 1440/1.5 = 960 rad/s^2

Average Angular Acceleration => Alfa = (w2-w1)/(t2-t1)= (0-1440)/1.5 = -960rad/s^2

wf=wi + alfa*(t) = > alfa = (wf-wi)/t ==> alfa = (0-1440)/1.5 = -960 rad/s^2


im almost sure about my results in the (Angular Velocity and Average Angular Velocity ) but for the (Angular Acceleration and Average Angular Acceleration i am not )

could someone correct my answers and explain the changes that has been made.

Thanx in Advance.

 

[Astronuc]

One is correct. One revolution is 360° or 2$\pi$ radians, and one correctly used the relationship $\pi$/180 rad/deg.

 

[uaeXuae]

Thanx but can anyone explain what is the correct angular acceleration (+960 or -960)and why ? and what is the difference in the pronouncings Average angular acceleration and angular acceleration hence

average speed = total distance / time.
average velocity = displacement / time.

 

[uaeXuae]

<up>

 

[rl.bhat]

Average velocity or acceleration is calculated if they are not uniform. In your problem there is no indication of that.

 

[uaeXuae]

Average velocity or acceleration is calculated if they are not uniform. In your problem there is no indication of that.

What do u mean not uniform ? and what is the indication or the thing that will make me know wheather its uniform or not ?
http://img516.imageshack.us/img516/3300/1234rr6.jpg

i still don't know how the second part is solved. Can someone clarify things to me ?

 

[rl.bhat]

Average Angular Velocity => w=(Theta2-Theta1)/(t2-t1)This is not true.
average angular velocity = total angular displacement / total time.

 

[uaeXuae]

ok
applying the law
average angular velocity = total angular displacement / total time.

average angular velocity = 1440/ 1.5 = 960


how is it -960 ?

 

[uaeXuae]

Average Angular Velocity => w=(Theta2-Theta1)/(t2-t1)This is not true.
average angular velocity = total angular displacement / total time.

and what would that


angular velocity be equal to in this case ?!

 

[rl.bhat]

Angular Velocity => w=(360*2)/0.5 = 1440 deg/s
1440 * (pi/180) = 23.132 rad/s. = Average angular velocity
Angular Acceleration => Alfa = (w)/(t)
Angular Acceleration => Alfa = 1440/1.5 = 960 rad/s^2
When the body comes to rest the acceleration cannot be positive.

 

[Astronuc]

ok
applying the law
average angular velocity = total angular displacement / total time.

average angular velocity = 1440/ 1.5 = 960


how is it -960 ?

As one worked out initially - Average Angular Acceleration => Alfa = (w2-w1)/(t2-t1)= (0-1440)/1.5 = -960rad/s^2

wf=wi + alfa*(t) = > alfa = (wf-wi)/t ==> alfa = (0-1440)/1.5 = -960 rad/s^2

The skater starts with an initial angular velocity wi at ti, and then decelerates to wf at tf.

The change in angular velocity is wf-wi and the change in time is tf-ti, and the angular acceleration is alfa = (wf-wi)/(tf-ti). If the body comes to rest, wf=0, to alfa = -wi/(tf-ti), and since tf > ti, the difference is positive, to the angular acceleration is negative.


w=(Theta2-Theta1)/(t2-t1) is correct, but one must be careful that Theta2 and Theta1 represent cumulative angular displacements from the same reference angle, and not just the angular displacement on a circle, i.e. Theta2 and Theta1 could > 360° or 2pi rad. In the given expression Theta2-Theta1 is the total angular displacement occurring between t2 and t1.

 

[uaeXuae]

thanx for your help but sorry for insisting ...

Angular Velocity => w=(360*2)/0.5 = 1440 deg/s

Understood

1440 * (pi/180) = 23.132 rad/s. = Average angular velocity

Thats just the same its converting from degree to radian( so converting from degree to radian is average angular velocity

Angular Acceleration => Alfa = (w)/(t)
Angular Acceleration => Alfa = 1440/1.5 = 960 rad/s^2

Not sure about that.

When the body comes to rest the acceleration cannot be positive.

Understood.


Once again why was the average angular velocity = 0 but there was a valus for the angular velocity. Not only that but what law should be used when calculating
Angular Acceleration & average Angular Acceleration.