# Combining translational and rotational velocities to get rotational velocity

aplysia

## 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?

## 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.

Homework Helper
Gold Member
Maybe this is the situation?

#### Attachments

• RotatingArm.JPG
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aplysia
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:
Homework Helper
Gold Member
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.

aplysia
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

Homework Helper
Gold Member
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
16.6 KB · Views: 475