If angular velocity of a disc depends an angle rotated $\theta$ as $\omega ={\theta }^2+2\theta$, then its angular acceleration $\alpha$ at $\theta =1$ rad is:

A spot light $S$ rotates in a horizontal plane with a constant angular velocity of $0.1 \mathrm{rad} {\mathrm{s}}^{-1}$. The spot of light $P$ moves along the wall at a distance $3\mathrm{m}$. What is the velocity of the spot $P$ when $\theta =45°$?

A particle $A$ moves along a circle of radius $R=50 \mathrm{cm}$ so that its radius vector $r$ relative to the point $O$ (figure) rotates with the constant angular velocity $\omega =0.40 \mathrm{rad} {\mathrm{s}}^{-1}$. Then modulus of the velocity of the particle, and the modulus of its total acceleration will be