A wheel has an angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2 s, it has rotated through an angle (in radian) of:
1. 6
2. 10
3. 12
4. 4

If a body is moving in a circular path with decreasing speed, then: (symbols have their usual meanings):

1.  $\overrightarrow{r}.\overrightarrow{\omega }$ $=$ $$ $0$

2.  $\overrightarrow{\tau }.\overrightarrow{v}$ $=$ $0$

3.  $\overrightarrow{a}.\overrightarrow{v}$ $<$ $0$

4.  All of these

Particles A and B are separated by 10 m, as shown in the figure. If A is at rest and B started moving with a speed of 20 m/s then the angular velocity of B with respect to A at that instant is:

The angular speed of the wheel of a vehicle is increased from \(360~\text{rpm}\) to \(1200~\text{rpm}\) in \(14\) seconds. Its angular acceleration will be: