What is the value of linear velocity, if angular velocity is 3 hat i - 4 hat j + hat k and distance from the centre is 5 hat i - 6 hat j + 6 hat k ?

Question

What is the value of linear velocity, if angular velocity is 3 hat i - 4 hat j + hat k and distance from the centre is 5 hat i - 6 hat j + 6 hat k ? (A) 6 hat i + 6 hat j - 8 hat k (B) -18 hat i - 13 hat j + 2 hat k (C) 4 hat i - 13 hat j - 6 hat k (D) 6 hat i - 2 hat j + 8 hat k

Tardigrade Admin · Accepted Answer

Linear vector v = ω × r Given, ω = 3 hat i - 4 hat j + hat k and r = 5 hat i - 6 hat j + 6 hat k ∴ v = | hat i hat j hat k 3 -4 1 5 -6 6 | = hat i (-24 + 6) - hat j (18 - 5) + hat k (-18 + 20) = -18 hat i - 13 hat j + 2 hat k

Q. What is the value of linear velocity, if angular velocity is $3 \hat{i} - 4 \hat{j} + \hat{k}$ and distance from the centre is $5 \hat{i} - 6 \hat{j} + 6 \hat{k}$ ?

$6 \hat{i} + 6 \hat{j} - 8 \hat{k}$

$- 18 \hat{i} - 13 \hat{j} + 2 \hat{k}$

$4 \hat{i} - 13 \hat{j} - 6 \hat{k}$

$6 \hat{i} - 2 \hat{j} + 8 \hat{k}$

Linear vector $v = ω \times r$
Given, $ω = 3 \hat{i} - 4 \hat{j} + \hat{k} an d r = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$
$∴ v = ∣ ∣ \hat{i} 35 \hat{j} - 4 - 6 \hat{k} 16 ∣ ∣$
$= \hat{i} (- 24 + 6) - \hat{j} (18 - 5) + \hat{k} (- 18 + 20)$
$= - 18 \hat{i} - 13 \hat{j} + 2 \hat{k}$

Q. What is the value of linear velocity, if angular velocity is 3i^−4j^​+k^ and distance from the centre is 5i^−6j^​+6k^ ?

6i^+6j^​−8k^

−18i^−13j^​+2k^

4i^−13j^​−6k^

6i^−2j^​+8k^