(C) In uniform circular motion,the velocity vector $\vec{v}$ is always perpendicular to the angular velocity vector $\vec{\omega}$.Therefore,their dot

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(C) In uniform circular motion,the velocity vector $\vec{v}$ is always perpendicular to the angular velocity vector $\vec{\omega}$.Therefore,their dot product must be zero: $\vec{v} \cdot \vec{\omega} = 0$.Given $\vec{v} = (6 \hat{i} - 2 \hat{j}) \ m/s$ and $\vec{\omega} = (a \hat{i} + b \hat{j}) \ rad/s$.Substituting these into the dot product equation:$(6 \hat{i} - 2 \hat{j}) \cdot (a \hat{i} + b \hat{j}) = 0$$6a - 2b = 0$$6a = 2b$$\frac{b}{a} = \frac{6}{2} = 3$.

Class 11 Physics 2 Motion in a Plane Angular Variables and Basic of Uniform Circular Motion

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$A$ particle is performing uniform circular motion. The velocity of the particle at an instant of time is $(6 \hat{i} - 2 \hat{j}) \ m/s$ and the angular velocity is $\vec{\omega} = (a \hat{i} + b \hat{j}) \ rad/s$. Then the value of $\frac{b}{a}$ is:

A
$2$
B
$12$
C
$3$
D
$-2$

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2 Motion in a Plane

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Angular Variables and Basic of Uniform Circular Motion

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$A$ particle moves so that its position vector is given by $\vec{r} = \cos(\omega t) \hat{i} + \sin(\omega t) \hat{j}$,where $\omega$ is a constant. Which of the following is true?

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$A$ particle is performing uniform circular motion. The velocity of the particle at an instant of time is $(6 \hat{i} - 2 \hat{j}) \ m/s$ and the angular velocity is $\vec{\omega} = (a \hat{i} + b \hat{j}) \ rad/s$. Then the value of $\frac{b}{a}$ is:

Similar Questions

If the linear speed of a particle moving in a circular path is constant,then the angular speed is proportional to (where $r$ is the radius of the circle):

For a particle in uniform circular motion,the acceleration $\vec{a}$ at a point $P(R, \theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x$-axis):

What is the angular velocity of the second hand of a clock?

$A$ body is revolving with a uniform speed '$v$' in a circle of radius '$r$'. The tangential acceleration is:

$A$ particle moves so that its position vector is given by $\vec{r} = \cos(\omega t) \hat{i} + \sin(\omega t) \hat{j}$,where $\omega$ is a constant. Which of the following is true?

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