Question

what is the value of linear velocity if w=3i-4j+k and r=5i-6j+6k?

Answer 1

Given: Angular velocity ω = 3 i- 4 j + k and position vector r = 5 i-6 j+6 k

To find: Linear velocity v =?

Concept: The linear velocity is defined as the cross product of angular velocity and position vector. That is

v = ω × r

v = ( - 24 + 6 ) i - (18 -5 ) j + ( -18 + 20 ) k

or, v = - 18 i - 13 j + 2 k

Now, we shall calculate the magnitude of linear velocity

$v = \sqrt{(-18)^{2}+(-13)^{2}+(+2)^{2}}\\ v = \sqrt{497} = 22.3$

Hence, the value of linear velocity will be v = - 18 i - 13 j + 2 k and its magnitude will 22.3 unit

Answer 2

Explanation:

The answer is give in the attachment..

For this sum, you have to know first about the vector product and dot product...