A couple produces:                                                               [NTSE 1995; CBSE PMT 1997; DCE 2004]

1. Purely linear motion

2. Purely rotational motion

3. Linear and rotational motion

4. No motion

A wheel is rotating at the rate of 33 rev/min.  If it comes to stop in 20 s. Then, the angular retardation will be

1. $\mathrm{\pi }\frac{\mathrm{rad}}{{\mathrm{s}}^2}$                         

2. $11\mathrm{\pi } \mathrm{rad}/{\mathrm{s}}^2$

3. $\frac{\mathrm{\pi }}{200} rad/s^2$             

4. $\frac{11\mathrm{\pi }}{200} rad/s^2$

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is 

1. 800 rad

2. 400 rad

3. 200 rad

4. 100 rad

A flywheel is in the form of a uniform circular disc of radius 1 m and mass 2 kg. The work which must be done on it to increase its frequency of rotation from 5 rev ${\mathrm{s}}^{-1}$ to 10 rev ${\mathrm{s}}^{-1}$ is approximately

1.  1.5 x ${10}^2$ J

2.  3.0 x ${10}^2$ J

3.  1.5 x ${10}^3$ J

4.  3.0 x ${10}^3$ J

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 radian and t is in second, then the angular velocity of the particle after 2s is 

1. 8 rad/s

2. 12 rad/s

3. 24 rad /s

4. 36 rad/s

A particle moves along a circle of radius $\frac{20}{\mathrm{\pi }}m$ with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is

1. 640 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

2. 160 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

3. 40 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

4. 40 $\mathrm{m}/{\mathrm{s}}^2$

A wheel has angular acceleration of 3.0 rad/$se{c}^2$ and an initial angular speed of 2.00 rad/sec.  In a time of 2 sec it has rotated through an angle (in radian) of 

1. 10               

2. 12

3. 4                 

4. 6

A homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 rad/sec. The linear momentum Of the disc is 

1.  1.2 kg m/sec 

2.  1.0 kg m/sec 

3.  0.6 kg m/sec 

4.  None of these

A rigid body rotates about a fixed axis with a variable angular velocity equal to \(\alpha\) \(-\) \(\beta t\), at the time t, where \(\alpha , \beta\) are constants. The angle through which it rotates before it stops is:

The motor of an engine is rotating about its axis with an angular velocity of 100 rpm.  It comes to rest is 15 s, after being switched off.  Assuming constant angular deceleration.  What are the numbers of revolutions made by it before coming to rest?

1. 12.5         

2. 40             

3. 32.6           

4. 15.6