Question

For hour body angular velocity w vector is equals to ICAP - 2 j cap + 3 k cap and radius vector r vector is equal ICAP + 2 j cap + k cap then its velocity is

Answer 1

Given: Two vectors: for angular velocity and radius vector.

To find: The velocity vector?

Solution:

• Now we have given the vectors which are as follows:

                   angular velocity (ω) = i - 2j + 3k

                   radius vector (r) = i + 2j + k

• Now we know the relation between linear velocity and angular velocity which is:

                  (ω) x (r) = v

• So putting the values in formula, we get:

                   v =  ( i - 2j + 3k ) x ( i + 2j + k )

                   v = $\left[\begin{array}{ccc}i&j&k\\1&-2&3\\1&2&1\end{array}\right]$

                   v = i(-2-6) - j(1-3) + k(2+2)

                   v = i(-8) - j(-2) + k(4)

                   v = -8i + 2j + 4k

Answer:

           So the velocity vector is -8i + 2j + 4k