# Angular Motion Question Understanding help ?

1. Nov 27, 2007

### uaeXuae

1. The problem statement, all variables and given/known data

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)?

2. Relevant 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)

3. 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.

2. Nov 27, 2007

### Staff: Mentor

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

3. Nov 27, 2007

### 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.

Last edited: Nov 27, 2007
4. Nov 28, 2007

### uaeXuae

<up>

5. Nov 28, 2007

### rl.bhat

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

6. Nov 28, 2007

### uaeXuae

What do u mean not uniform ? and what is the indication or the thing that will make me know wheather its uniform or not ?

i still dont know how the second part is solved. Can someone clarify things to me ?

7. Nov 28, 2007

### rl.bhat

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

8. Nov 28, 2007

### uaeXuae

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

average angular velocity = 1440/ 1.5 = 960

how is it -960 ?

9. Nov 29, 2007

### uaeXuae

and what would that

angular velocity be equal to in this case ?!

10. Nov 29, 2007

### 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.

11. Nov 29, 2007

### Staff: Mentor

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 occuring between t2 and t1.

12. Nov 29, 2007

### uaeXuae

thanx for your help but sorry for insisting ...

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