The angular acceleration of a body, moving along the circumference of a circle, is :

The wheel of a car is rotating at the rate of $1200$ revolutions per minute. On pressing the accelerator for $10 \ s$,it starts rotating at $4500$ revolutions per minute. The angular acceleration of the wheel is:

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 $^{\circ}$)

An athlete throws a discus from rest to a final angular velocity of $15 \, rad \, s^{-1}$ in $0.270 \, s$ before releasing it. During acceleration,the discus moves along a circular arc of radius $0.810 \, m$. The acceleration of the discus before it is released is ....... $m \, s^{-2}$.

$A$ wheel of radius $30 \ cm$ is driven by a belt. Its initial angular speed is $2 \ rev/s$. Starting at this speed,it comes to rest after a length of $25 \ m$ of the belt has passed over the wheel. The angular deceleration of the wheel is ....... $rad \ s^{-2}$.

The angular speed of a motor wheel is increased from $1200 \; rpm$ to $3120 \; rpm$ in $16 \; s$.
$(i)$ What is its angular acceleration,assuming the acceleration to be uniform?
$(ii)$ How many revolutions does the engine make during this time?