Question

a particle is located at (3m,4m) and moving with velocity v=

Answer 1

Ans-3

Component the velocity perpendicular to R vector.

Answer 2

The correct answer is -k

Given,

Location of particle, r = (3m, 4m)

Velocity of the particle, v = $(4 \hat{i} - 3 \hat{j})$ m/s

To Find,

Angular velocity, ω

Solution,

Given, the location of particle, r = (3m, 4m)

$\implies r = (3\hat{i} + 4\hat{j})$

Also, $v = (4 \hat{i} - 3 \hat{j})$

We know that angular velocity is the ratio of component of velocity perpendicular to r and r itself

$r \times v = (3\hat{i} + 4\hat{j})(4\hat{i} - 3\hat{j}) = 0$

Since r × v = 0,

⇒ v ⊥ r

⇒ ω = v/r

|v| = √(3² + 4²) = √(9+16) = √(25) = 5

|r| = √(4² + 3²) = √(16+9) = √(25) = 5

⇒ |ω| = 5/5 = 1

Also, angular velocity is along the negative z axis based on the axis of rotation

Therefore, the angular velocity about the origin in -k

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