Question

An object is moving in three dimensions, following a circular path at a constant radius from the origin, with a constant angular velocity ω--Зі + k. If its linear velocity is expressed as v-vi + vyj+ vzk, what is the value of vy at the moment when its position vector is r-i+ 2j - 3k?

Answer 1

`v_y = -8 m/s`

Step-by-step explanation:

As we know that due to rotational motion the linear velocity of any point is given as

`\vec v = \vec \omega * \vec r`

here we know that

`\vec \omega = -3\hat i + \hat k`

`\vec r = \hat i + 2\hat j - 3\hat k`

now we have

`\vec v = (-3\hat i + \hat k) * (\hat i + 2\hat j - 3\hat k)`

`\vec v = -6\hat k - 9\hat j + \hat j - 2\hat i`

`\vec v = -2\hat i - 8\hat j - 6\hat k`

So y component of velocity is given as

`v_y = -8 m/s`