For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and angular velocity $\omega$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ is $.................$.
For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and angular velocity $\omega$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ is $.................$.
- [JEE MAIN 2023]
- A
$x(t)=r \cos \left(\omega t+\frac{\pi}{6}\right)$
- B
$x(t)=r \cos (\omega t)$
- C
$x(t)=r \sin \left(\omega t+\frac{\pi}{6}\right)$
- D
$x(t)=r \cos \left(\omega t-\frac{\pi}{6} \omega\right)$
Similar Questions
A particle moving in a circle of radius $R$ with uniform speed takes time $\mathrm{T}$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4 R$. The angle of projection $\theta$ is then given by :
A particle moving in a circle of radius $R$ with uniform speed takes time $\mathrm{T}$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4 R$. The angle of projection $\theta$ is then given by :
- [JEE MAIN 2024]
An athlete completes one round of a circular track of radius $10\, m$ in $40\, sec$. The distance covered by him in $2 \,min$ $20 \,sec$ is ........ $m$
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A particle is moving with constant speed $v$ in $x y$ plane as shown in figure. The magnitude of its angular velocity about point $O$ is .........
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If the equation for the displacement of a particle moving on a circular path is given by $(\theta) = 2t^3 + 0.5$, where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particle after $2\, sec$ from its start is ......... $rad/sec$
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