# Combining rotational and translational velocities

1. Sep 23, 2012

### aplysia

Hi, I need help with a homework problem, because I am unsure in what way rotational and translational velocity combine.
Also, I can not really imagin ethe movement described in the problem, so I am not sure how to start
1. The problem statement, all variables and given/known data
At some instant a person’s forearm has a rotational velocity of (2, 1, 4), the elbow has translational
velocity (1, 0, 0) and the wrist is at location (0, 1, 1) relative to the elbow. What is the translational
velocity of the wrist?

2. Relevant equations
v = w X r
3. The attempt at a solution
when substituting the rotational velocity for w, the velocity and the velocity of the elbow for v, I get a system of 3 equations with three unknown variables that can not be solved.
So I know that translational velocities just add by vector addition, but that rotational velocities are non-commutative, so I can not just add them. But in this case, one vector is rotational, so I don't know how to combine this two velocity vectors.
Also, I am not sure about the given date, because it is not stated if the translational velocity of the elbow is caused by the rotational velocity of the forearm.
So probably I miss something quite obvious here, but your help would be really appreciated,