Question

If r=4i and angular velocity=4k then linear velocity=?

Answer 1

The formula is

linear velocity v = radius r x angular velocity w

v = 4i x 4 k
v = - 16 j


(Note that i x j = k , j x k = i and k x i = j which are the properties of vector cross products. )

Also note that if the order is changed we need to put a minus sign. To illustrate,

i x j = k but j x i = -k
Thus i x k = - k x i = - j


Hope this helps.

Answer 2

Answer:

The linear velocity of the body will be 16j.

Explanation:

When a particle moves on a circular path with constant speed, then its motion is said to be a uniform circular motion.

The rate of angular displacement undergone by a particle performing uniform circular motion is called its angular velocity.

Relation between Angular velocity and Linear velocity

          $angular velocity = \frac{linear velocity}{distance of particle from centre}$  

                               ω = v/r

Thus, for a given angular velocity, the linear velocity of the particle is directly proportional to the distance of the particle from the center.

In vector form

                $\vec{v} =\vec{ \omega} \times \vec{r}$

                $\vec{v} =4k\times 4i$

The vector product of unit orthogonal vectors i, j, and k have the following relations

  i×j = k

  j×k = i

  k×i = j

 so we have,

                     $\vec{v} =4k\times 4i\\\vec{v} = 16j$

learn more

circular motion:https://brainly.in/question/3822180

vector product : https://brainly.in/question/9110318