Questions in rotational-motion

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A strap is passing over a wheel of radius 30 cm. During the time the wheel moving with initial constant velocity of 2 rev/sec. comes to rest the strap covers a distance of 25 m. The deceleration of the wheel in $rad/s^2$ is
A particle starts rotating from rest. Its angular displacement is expressed by the following equation $\theta =0.025{{t}^{2}}-0.1t$ where $\theta $ is in radian and t is in seconds. The angular acceleration of the particle is
The planes of two rigid discs are perpendicular to each other. They are rotating about their axes. If their angular velocities are 3 rad/sec and 4 rad/sec respectively, then the resultant angular velocity of the system would be
A sphere is rotating about a diameter
A rigid body is rotating with variable angular velocity $(a-bt)$ at any instant of time t. The total angle subtended by it before coming to rest will be (a and b are constants)
When a ceiling fan is switched on, it makes 10 rotations in the first 3 seconds. How many rotations will it make in the next 3 seconds (Assume uniform angular acceleration)
When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest (Assume uniform angular retardation)
Let $\overset{\to }{\mathop{A}}\,$ be a unit vector along the axis of rotation of a purely rotating body and $\overset{\to }{\mathop{B}}\,$ be a unit vector along the velocity of a particle P of the body away from the axis. The value of $\overset{\to }{\mathop{A}}\,.\overset{\to }{\mathop{B}}\,$ is
Let F be the force acting on a particle having position vector $\vec{r}\,a\text{nd }\vec{T}$ be the torque of this force about the origin. Then
A couple produces

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