The angular speed of a truck wheel is increased from $900 \, rpm$ to $2460 \, rpm$ in $26 \, s$. The number of revolutions made by the truck engine during this time is (assuming the acceleration to be uniform).

$A$ wheel rotates with a constant angular acceleration. The initial angular velocity is zero. It covers an angular displacement of ${\theta _1}$ in the first $2 \, s$ and ${\theta _2}$ in the next $2 \, s$. Then,the ratio $\frac{{\theta _1}}{{\theta _2}}$ is equal to:

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 $^{\circ}$)

$A$ wheel has an angular acceleration of $3.0\, rad/s^2$ and an initial angular speed of $2.00\, rad/s$. In a time of $2\, s$,it has rotated through an angle (in radians) of:

$A$ body rotating with an angular speed of $600 \, rpm$ is uniformly accelerated to $1800 \, rpm$ in $10 \, s$. The number of rotations made in the process is ..... .

$A$ ceiling fan starts from rest and makes $10$ revolutions in the first $3$ seconds. If the angular acceleration remains constant,how many revolutions will it make in the next $3$ seconds?