Calculate: the torque of a force \(\left(5\hat{i}-2\hat{j}+5\hat{k}\right)\) about the origin which acts on a particle whose position vector is \(\left(\hat{i}+\hat{j}-2\hat{k}\right)\).
A particle of mass \(m\) is moving along a straight line parallel to x-axis at a distance b with constant speed v. Find the angular momentum of particle at time t w.r.t origin. What do you conclude from the calculated value?
Ans: \(\vec{L}=-\left(mvb\right)\hat{k}\).
A particle of mass m is moving in X-Y plane with its uniform velocity \(v\) in a trajectory parallel to x-axis and intersection y-axis at \(y=b\) as shown in below figure. the particle bounces elastically from the wall just opposite to the x-axis. calculate: change in angular momentum of the particle.
Ans: \(\Delta\vec{p}=\left(2mvb\right)\hat{k}\) .
A \(3m\) long ladder weighing \(20kg\) leans on a frictionless wall. Its feet rests on the floor \(1m\) from the wall as shown in figure. Find: the reaction force of the wall and the floor.
Ans: \(F_{2}=199.00N\) and \(\alpha=tan^{-1}\left(5.6568\right)=80^{o}\).
Show that the angular momentum of a satellite of mass \(M_{s}\) revolving around the earth having mass \(M_{e}\) in an orbit of radius \(r\) is \(L=\sqrt{GM_{e}M_{s}r}\).
A car of mass \(2500kg\) is moving in a circular track of diameter \(100m\) with a speed of \(72\frac{km}{hr}\). What is angular momentum of car?
A torque of \(10^{4}Nm\) acting on a rigid body, turns it through \(60^{o}\) in \(0.2s\). calculate: the work done by the torque on the body and power delivered by the torque.
Ans: \(\left(1.04\times10^{4}\right)J\) and \(\left(5.2\times10\right)W\).
