If a wheel completes 10 rotations in 5 seconds, what is its average angular speed in rad/s?

Two particles of masses ${m_1}\,and\,{m_2}$ in projectile motion have velocities ${{\rm{\vec v}}_1}\,and\,{{\rm{\vec v}}_2}$ respectively at time t=0. They collide at time ${t_0}$. Their velocities become {{\rm{\vec v'}}_1}\,and\,{{\rm{\vec v'}}_2} at time $2{t_0}$ while still moving in air. The value of \left[ {\left( {{m_1}{{{\rm{\vec v'}}}_1} + {m_2}{{{\rm{\vec v'}}}_2}} \right) - \left( {{m_1}{{{\rm{\vec v}}}_1} - {m_2}{{{\rm{\vec v}}}_2}} \right)} \right]

The angular displacement 'θ' of a rotating body is related to time 't' by the equation $heta = 2t + 3t^2$. What is the angular acceleration at t = 2s?

In an elastic head on collision between two particles

Consider a two particle system with particles having masses ${m_1}\,and\,{m_2}$. If the first particles is pushed towards the centre of mass through a distance $d$, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

A particle is moving with uniform speed $0.5\,m/s$ along a circle of radius $1m$, then the angular velocity of particle is ( in $rad{s^{ - 1}}$)

Two bodies A and B have masses M and m respectively, where $M > m$ and they are at a distance d apart. Equal force is applied to them so that they approach each other. The position where they hit each other is

Two bodies of masses 2 kg and 4 kg are moving with velocities 20 ${\rm{m}}{{\rm{s}}^{ - 1}}$ and 10 ${\rm{m}}{{\rm{s}}^{ - 1}}$ towards each other due to mutual gravitation attraction. What is the velocity of their centre of mass?

Two stars of mass ${m_1}\,and\,{m_2}$ are part of a binary star system. The radii of their orbits are ${r_1}\,and\,{r_2}$ respectively, measured from the C.M. of the system. The magnitude of acceleration of ${m_1}$ is

A figure skater spins with her arms outstretched. When she pulls her arms inwards, her angular velocity increases. This is due to:

Two blocks of masses 10 kg and 4 kg connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $14{\rm{\;m}}{{\rm{s}}^{ - 1}}$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is