The velocity $\vec{v}$ of a particle of mass $m$ acted upon by a constant force is given by $\vec{v}(t) = A[\cos(kt) \hat{i} - \sin(kt) \hat{j}]$. Then the angle between the force and the velocity of the particle is (Here $A$ and $k$ are constants). (in $^{\circ}$)

$A$ body moves with a constant angular velocity on a circle. What is the magnitude of its angular acceleration?

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

$A$ fan is rotating with an angular speed of $300 \text{ rpm}$. The fan is switched off,and it takes $80 \text{ s}$ to come to rest. Assuming constant angular deceleration,the number of revolutions made by the fan before it comes to rest is:

$A$ ball is spun with angular acceleration $\alpha = 6t^2 - 2t$,where $t$ is in seconds and $\alpha$ is in $rad/s^2$. At $t = 0$,the ball has an angular velocity of $10 \ rad/s$ and an angular position of $4 \ rad$. The most appropriate expression for the angular position of the ball is:

$A$ clock has $75 \ cm$ and $60 \ cm$ long second hand and minute hand respectively. In $30$ minutes duration,the tip of the second hand will travel $x$ distance more than the tip of the minute hand. The value of $x$ in meters is nearly (Take $\pi = 3.14$):