Combining translational and rotational velocities to get rotational velocity

In summary, the conversation is discussing the rotational velocity of a person's forearm in space when their upper arm is rotating relative to space at 2 radians/s and their elbow is flexing at 2 radians/s. The question is whether the rotational velocity of the forearm is measured at a specific point or if it refers to the angular velocity of the entire forearm. The conversation then uses an example of a spinning teacup ride to explain the concept of rotational velocity relative to a rotating platform and how it can be applied to the forearm situation.
  • #1
aplysia
4
0

Homework Statement



Suppose you are standing uptight with your right arm stretched out straight in front of you, palm down, the upper arm rotating rightward relative to space at 2 radians/s and the elbow flexing in the horizontal plane at 2 radians/s. What is the rotational velocity of the forearm in space?

Homework Equations





The Attempt at a Solution


I am not sure if I understood the description of the movement correctly, because now I have the impression that there are informations missing I would need to solve this, e.g, on which point on the forearm the rotational velocity is measured, because I thuoght that would depent on the point on the forearm.
 
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  • #2
Maybe this is the situation?
 

Attachments

  • RotatingArm.JPG
    RotatingArm.JPG
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  • #3
Thanks, that might indeed be the situation, my main problem is really that I am not sure if I understand the descprition of the problem.
What also confuses me is what rotation of forearm relative to space means in this context the velocity of on specific point on the forearm or if it refers to the angular velocity of the forarm.
I know that angular velocity is given by v=w*r, but I alway thought I needed some kind of reference point r to calculate angular velocities.
Also I am unsure of how to combine rotational and translational velocities
any hint to find the right approach is greatly appreciated,
aplysia
 
Last edited:
  • #4
I think you just want angular velocity. So, no need to pick a specific point on the arm or worry about v. Rotational velocity relative to space is the same as angular velocity relative to the room the person stands in.
 
  • #5
Then I really do not understand how the rotational velocity of the shoulder and the translational velocity of the elbow are related to each other and how they result in the rotatinal velocity, maybe I miss something really obvious here, but right now, I can't see how they result in the rotational velocity
 
  • #6
Hope my interpretation of the problem is correct.

Remember when you rode the Spinning Teacup amusement park ride? (One of my favorites.) See attachment.

Suppose that the green platform that the cups are riding on is rotating clockwise at 2 rad/s and suppose one of the teacups is rotating counterclockwise at 2 rad/s relative to the green platform. At what rate would the teacup rotate relative to the ground?
 

Attachments

  • SpinningTeacups.jpg
    SpinningTeacups.jpg
    16.6 KB · Views: 510

1. What is translational velocity?

Translational velocity is the speed at which an object moves in a straight line. It is measured in units of distance per time, such as meters per second or miles per hour.

2. What is rotational velocity?

Rotational velocity is the speed at which an object rotates around an axis. It is measured in units of angle per time, such as radians per second or revolutions per minute.

3. How are translational and rotational velocities combined to get rotational velocity?

To combine translational and rotational velocities, you first need to determine the distance between the axis of rotation and the point of interest on the object. Then, you multiply the translational velocity by the distance to get the linear speed at that point. Finally, you divide the linear speed by the radius to get the rotational velocity.

4. What is the importance of combining translational and rotational velocities?

Combining translational and rotational velocities allows us to fully understand the movement of an object. It helps us determine the direction and speed of both the linear and rotational motion, which is crucial for various applications such as navigation, robotics, and sports analysis.

5. Can rotational velocity be negative?

Yes, rotational velocity can be negative. A negative rotational velocity indicates that the object is rotating in the opposite direction of its positive value. This can occur when the object is slowing down or changing direction.

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