A particle is moving in a circle of radius 0.5 m with a constant angular speed of 2 rad/s. What is its linear speed?

A solid sphere, disc and solid cylinder all of the same mass are made of the same material are allowed to roll down (from rest) on an inclined plane, then

In a bicycle the radius of rear wheel is twice the radius of front wheel. If ${r_F}\,and\,{r_r}$ are the radius, ${v_F}\,and\,{v_r}$, are speeds of top most points of wheel, then

The angular displacement of a body is given by $heta = 2t^3 + 0.5t^2$. What is its angular velocity at $t=1$ s?

A flywheel of radius 0.5 m, initially at rest, begins to rotate with a constant angular acceleration of 2 rad $s^{-2}$. What is its net acceleration (in $ms^{-2}$) at a point on its rim after 2 seconds?

A flywheel's angular speed increases uniformly from 1200 rpm to 3120 rpm in 16 seconds. Calculate its angular acceleration in $\rad/s^2$.

Two identical discs are rotating about their axes with angular speeds $\omega_1$ and $\omega_2$. They are brought into contact face to face with their axes of rotation coincident. The final angular speed of the system is:

A mass is revolving in a circle which is in the plane of paper. The direction of angular acceleration is

A uniform circular disc of radius 50 cm at rest is free to tum about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad ${{\rm{s}}^{{\rm{ - 2}}}}$. Its net acceleration in ${\rm{m}}{{\rm{s}}^{{\rm{ - 2}}}}$ at the end of 2.0 is approximately.

A particle moves along a circle of radius $\frac{{20}}{\pi }m$ 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

A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are