For a particle in uniform circular motion, the acceleration $\overrightarrow{ a }$ at any point $P ( R , \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x\,-$axis and $v$ is uniform speed)
$-\frac{v^{2}}{R} \sin \theta \hat{i}+\frac{v^{2}}{R} \cos \theta \hat{j}$
$-\frac{v^{2}}{R} \cos \theta \hat{i}+\frac{v^{2}}{R} \sin \theta \hat{j}$
$-\frac{v^{2}}{R} \cos \theta \hat{i}-\frac{v^{2}}{R} \sin \theta \hat{j}$
$-\frac{v^{2}}{R} \hat{i}+\frac{v^{2}}{R} \hat{j}$
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
During which time interval is the particle described by these position graphs at rest?
A projectile is given an initial velocity of $(\hat i+2\hat j)\,m/ s$ where $\hat i$ is along the ground and $\hat j$ is along the vertical. If $g = 10\,m/s^2,$ the equation of its trajectory is
Average velocity of a particle is projectile motion between its starting point and the highest point of its trajectory is : (projection speed = $u$, angle of projection from horizontal= $\theta$)
The co-ordinates of a moving particle at a time $t$, are give by, $x = 5 sin 10 t, y = 5 cos 10t$. The speed of the particle is :