The angular speed of a motor wheel is increased from $1200 rpm$ to $3120 rpm$ in $16 s$. The angular acceleration of the motor wheel is

The moment of inertia of a wheel about its vertical axis is $2 \ kg \ m^2$. It is rotating about this axis at a speed of $60 \ rpm$. What torque must be applied to bring the wheel to rest in $1 \ minute$?

$A$ rectangular solid rod of length $0.3\, m$ is held horizontally,with one of its sides on the edge of a platform of height $5\, m$. When released,it slips off the table in a very short time $\Delta t = 0.01\, s$,remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?

$A$ constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4 A_0$ in $4$ seconds. The magnitude of this torque is ...........

$A$ uniform rod of length $l$,hinged at the lower end,is free to rotate in the vertical plane. If the rod is held vertically in the beginning and then released,what is the angular acceleration of the rod when it makes an angle of $45^{\circ}$ with the horizontal? (Given: Moment of inertia $I = ml^2/3$)