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

In summary, the conversation is about determining the speed of a skater's outstretched arms as she spins at 120rpm with her hands 130cm apart. The solution involves using the relationship between linear velocity, radius, and angular velocity, as well as converting rpm to rps. The final answer may have slight variations due to round off accuracy.
  • #1
mmbruns
7
0
A skater holds her arms outstretched as she spins at 120rpm. What is the speed of her hands if they are 130cm apart?
 
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  • #3
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
 
  • #4
I Got It!

Thanks for your help!
 
  • #5
Nope didn't get it...I tried doing the equation v=w(pi)f wrong! Gerrrrr
 
  • #6
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[itex]\pi[/itex] radians, which is a measure of angle.

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

Now apply the formula - Vt=Angular velocity * radius.
 
  • #7
The answer I get from that is 0.81705
 
  • #8
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.
 
  • #9
I understand that, but that is not the answer...I tried it already.
 
  • #10
For Future reference, the equation for this problem is V=[2(pi)r]/t

t is found per second
i.e. 60/120
 
  • #11
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.
 

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or a fixed point. This type of motion is typically seen in objects such as wheels, gears, and spinning tops.

2. What are the basic principles of rotational motion?

The basic principles of rotational motion include torque, angular velocity, and angular acceleration. Torque is the force that causes an object to rotate, while angular velocity is the rate at which the object rotates. Angular acceleration is the change in angular velocity over time.

3. How is rotational motion different from linear motion?

Rotational motion involves movement in a circular or curved path, while linear motion involves movement in a straight line. Additionally, rotational motion involves the use of angular measurements, such as radians, while linear motion typically uses distance measurements, such as meters.

4. What are some real-life examples of rotational motion?

Examples of rotational motion in daily life include the rotation of the Earth around its axis, the spinning of a car tire, and the movement of a ceiling fan.

5. How is rotational motion related to energy?

Rotational motion involves the transfer of energy from one form to another. For example, when a spinning top slows down, its kinetic energy is converted into potential energy. Additionally, rotational motion can also be used to generate energy, such as in the case of wind turbines and hydroelectric dams.

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