What is the value of linear velocity if \(\vec{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\vec{r} = 5\hat{i} - 6\hat{j} + 6\hat{ k}\):

1.	\(6 \hat{i}+2 \hat{j}-3 \hat{k} \)
2.	\(-18 \hat{i}-13 \hat{j}+2 \hat{k} \)
3.	\(4 \hat{i}-13 \hat{j}+6 \hat{k}\)
4.	\(6 \hat{i}-2 \hat{j}+8 \hat{k}\)

A particle moves with constant speed \(v\) along a circular path of radius \(r\) and completes the circle in time \(T\). The acceleration of the particle is:
1. \(2\pi v / T\)
2. \(2\pi r / T\)
3. \(2\pi r^2 / T\)
4. \(2\pi v^2 / T\)

If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if:
1. a_r = 0 and a_t = 0
2. a_r = 0 but a_t \(\neq\) 0
3. a_r \(\neq\) 0 but a_t = 0
4. a_r \(\neq\) 0 and a_t \(\neq\) 0$\mathrm{}$
 

          
1. \(3.14~\text{m/s}\)
2. \(2.0~\text{m/s}\)
3. \(1.0~\text{m/s}\)
4. zero

A stone tied to the end of a string of \(1\) m long is whirled in a horizontal circle with a constant speed. If the stone makes \(22\) revolutions in \(44\) s, what is the magnitude and direction of acceleration of the stone?

If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where \(\theta\) is in radians and \(t\) in seconds, then the angular velocity of the particle after \(2\) sec from its start is:
1. \(8\) rad/sec
2. \(12\) rad/sec
3. \(24\) rad/sec
4. \(36\) rad/sec

For a particle in a non-uniform accelerated circular motion 

1. Velocity is radial and acceleration is transverse only

2. Velocity is transverse and acceleration is radial only

3. Velocity is radial and acceleration has both radial and transverse components

4. Velocity is transverse and acceleration has both radial and transverse components

The coordinates of a moving particle at any time \(t\) are given by \(x= \alpha t^3\) and \(y = \beta t^3.\) The speed of the particle at a time \(t\) is given by:

A particle moves in a circular path with decreasing speed. Choose the correct statement. 

(1) Angular momentum remains constant

(2) Acceleration ($\overrightarrow{a}$) is towards the center

(3) Particle moves in a spiral path with decreasing radius

(4) The direction of angular momentum remains constant

The angle turned by a body undergoing circular motion depends on time as $\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$. Then the angular acceleration of the body is 

(1) θ₁

(2) θ₂

(3) 2θ₁

(4) 2θ₂