NCERT Solutions for Chapter: Systems of Particles and Rotational Motion, Exercise 4: SA

The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point?

A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However, the particles that constitute the wheel do experience a centripetal acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium? How would you set a half-wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion?

A door is hinged at one end and is free to rotate about a vertical axis . Does its weight cause any torque about this axis? Give reason for your answer.

$(n-1)$ equal point masses each of mass $m$ are placed at the vertices of a regular $n$ polygon. The vacant vertex has $a$ position vector $\overrightarrow{a}$ with respect to the centre of the polygon. Find the position vector of centre of mass.