SATHEE: Motion in a Plane - Result Question 13

Motion in a Plane - Result Question 13

15. What is the linear velocity if angular velocity vector $\vec{ω} = 3 \hat{i} - 4 \hat{j} + \hat{k}$ and position vector $\vec{r} = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$

[1999]

(a) $6 \hat{i} + 2 \hat{j} - 3 \hat{k}$

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

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

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Answer:

Correct Answer: 15. (b)

Solution:

(b) As we know that

$\begin{aligned} \vec{v} & = \vec{ω} \times \vec{r} = (3 \hat{i} - 4 \hat{j} + \hat{k}) \times (5 \hat{i} - 6 \hat{j} + 6 \hat{k}) \\ = - 18 \hat{i} - 13 \hat{j} + 2 \hat{k} \end{aligned}$

Motion in a Plane - Result Question 13

15. What is the linear velocity if angular velocity vector $\vec{ω} = 3 \hat{i} - 4 \hat{j} + \hat{k}$ and position vector $\vec{r} = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$

Answer:

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Motion in a Plane - Result Question 13

15. What is the linear velocity if angular velocity vector ω→=3i^−4j^+k^ and position vector r→=5i^−6j^+6k^

Answer:

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15. What is the linear velocity if angular velocity vector $\vec{ω} = 3 \hat{i} - 4 \hat{j} + \hat{k}$ and position vector $\vec{r} = 5 \hat{i} - 6 \hat{j} + 6 \hat{k}$