Reasoning: Centrifugation is a method of separating components of a mixture by rapid spinning. Heavier particles move outward / downward faster, while lighter particles remain above.

Reasoning: The tendency to overturn on a curve depends on centripetal force, and centripetal force is proportional to the square of speed:
$\mathbf{F}_{\mathbf{c}}\mathbf{\propto}$ $\mathbf{v}^{\mathbf{2}}$
So, if speed becomes double, the tendency becomes:
$\mathbf{(2v)}^{\mathbf{2}}\mathbf{=}$ $\mathbf{4}\mathbf{v}^{\mathbf{2}}$
Therefore, it is quadrupled.

Reasoning: Moment of inertia depends on the mass of the body, distribution of mass around the axis, and orientation of the axis. It does not depend on how fast the body is rotating, so it does not depend on angular velocity.

Reasoning: Change in angular momentum is equal to torque multiplied by time:
$\mathbf{\Delta L =}\mathbf{\tau t}$ $\mathbf{\Longrightarrow}$ $\mathbf{\Delta L = 2.5 \times 2 = 5\, Js}$
So, the change in angular momentum is $\mathbf{5\ Js}$.

Reasoning: If the length of fan wings increases, the mass spreads farther from the axis. This increases the moment of inertia. With the same voltage and current, the fan has the same power supply, so it becomes harder to rotate fast. Therefore, rotational speed decreases.

Reasoning: In linear motion, acceleration is produced by net force. In rotational motion, angular acceleration is produced by net torque:
$\mathbf{\tau =}$ $\mathbf{I}\mathbf{\ }\mathbf{\alpha}$
So, angular acceleration is caused by net torque.

Reasoning: An astronaut feels weightless inside the ISS because both the astronaut and the ISS are continuously falling freely around Earth. Gravity is still present there, but everything falls together, so the astronaut feels weightless.

Reasoning: One complete circle has an angle of $\mathbf{360}^{\mathbf{o}}$, which is equal to:
$\mathbf{\Longrightarrow}$ $\mathbf{2\pi}$ $\mathbf{radian}\mathbf{s}$
So, the circumference of a circle corresponds to $\mathbf{2\pi}$ $\mathbf{radian}\mathbf{s}$.

Reasoning: Angular acceleration $\overrightarrow{\mathbf{\alpha}}$ is defined as the rate of change of angular velocity:
$\mathbf{\Longrightarrow}$ $\overrightarrow{\mathbf{\alpha}}\mathbf{=}$ $\frac{\mathbf{\mathrm{\Delta}}\overrightarrow{\mathbf{\omega}}}{\mathbf{\mathrm{\Delta}t}}$
Also, for rotational motion: $\overrightarrow{\mathbf{v}}\mathbf{=}\overrightarrow{\mathbf{\omega}}\mathbf{\times}\overrightarrow{\mathbf{r}}$
and tangential acceleration is: $\overrightarrow{\mathbf{a}_{\mathbf{t}}}\mathbf{=}\overrightarrow{\mathbf{\alpha}}\mathbf{\times}\overrightarrow{\mathbf{r}}$
Therefore, $\overrightarrow{\mathbf{\alpha}}\mathbf{=}\overrightarrow{\mathbf{v}}\mathbf{\times}\overrightarrow{\mathbf{r}}$ is not a correct relation.