What is the speed of the skater's hands in rotational motion?

[mmbruns]

A skater holds her arms outstretched as she spins at 120rpm. What is the speed of her hands if they are 130cm apart?

 

[Astronuc]

Please show some effort and work on the solution of this problem.

One needs to determine the angular velocity from the rpm.

For that, use the relationship between linear (tangential) velocity, the radius, and angular velocity.

Please refer to - http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html

and http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

 

[mmbruns]

Work.

From what I understand in class

Vt=Angular velocity * radius

from my calculations

120rpm = 2rps
and
d=.130m, so C= .4082m

And I multiplied

2*.4082 to find the total distance in one revolution

=.8164m in one sec

Now I'm stuck

 

[mmbruns]

I Got It!

Thanks for your help!

 

[mmbruns]

Nope didn't get it...I tried doing the equation v=w(pi)f wrong! Gerrrrr

 

[Astronuc]

Well one has the answer - =.8164m in one sec => 0.8164 m/s!

rpm is revolutions per minute and rps is revolutions per second.

Now in one revolution, a point on the circumference travels 2$\pi$ radians, which is a measure of angle.

So 2 rps = 2 * 2$\pi$ rad/s = 12.57 rad/s, which is $\omega$, the angular velocity.

Now apply the formula - Vt=Angular velocity * radius.

 

[mmbruns]

The answer I get from that is 0.81705

 

[Astronuc]

Yes. There is round off accuracy involved in both calculations.

If one uses 12.566 (4 pi) instead of 12.57 rad/s, then the answer becomes 0.8168 m/s.

 

[mmbruns]

I understand that, but that is not the answer...I tried it already.

 

[mmbruns]

For Future reference, the equation for this problem is V=[2(pi)r]/t

t is found per second
i.e. 60/120

 

[KatlynEdwards]

Hmm the answer of 0.82 doesn't seem to be correct according to Mastering Physics. I've followed the steps provided, and I still can't seem to figure out where we're going wrong. Any help would be appreciated.