A fly wheel completes \(240\) revolutions per minute. Calculate: its angular speed?
Ans: \(\omega= 8\pi rad.s^{-1}\).
A car goes around a circular track of radius \(20m\) with a speed \(20ms^{-1}\). What will be angular speed of car?
Ans: \(\omega= 1 rad.s^{-1}\).
A particle goes around a circular orbit of radius \(10cm\) at \(120rpm\). Calculate: Acceleration of the particle?
Ans: \(\alpha= 160\pi^{2} cm.s^{-2}\)
Which is greater, the angular speed of hour hand \(\left(\omega_{1}\right)\) of watch or the angular speed of earth \(\left(\omega_{2}\right)\) about its polar axis? Also, find their ration?
Ans: \(\omega_{1}>\omega_{2}\).
An insect is trapped in a circular groove of radius \(12cm\), and moving along the groove steadily and completes \(7\) revolutions \(100Sec\) . What will be the (i) angular speed and (ii) linear speed of the insect?
Ans:(i) \(\omega=0.44rad.s^{-1}\) (ii) \(v=5.28 cm.s^{-1}\).
A particle is moving uniformly in a circular path of radius \(r\). When it moves through an angular displacement \(\theta\), then what is the magnitude of its linear displacement?
Ans: \(2rSin\frac{\theta}{2}\).
A threaded rod with \(12\) turns per cm and diameter \(1.18cm\) is mounted horizontally. A bar with a threaded hole to match the rod is screwed on to the rod. The bar spins at a rate of \(216rpm\). How long it will take for the bar to move \(1.15cm\) along the rod?
Ans: \(Time=5Sec\).
What is the value of linear velocity. If, given: \(\vec{\omega}=\left(3\hat{i}-4\hat{j}+\hat{k}\right)\) and \(\vec{r}=\left(5\hat{i}-6\hat{j}+6\hat{k}\right)\).
The velocity of a particle moving in the x-y plane is given by, \(\frac{dx}{dt}=8\pi\sin\left(2\pi.t\right)\) and \(\frac{dy}{dt}=5\pi\cos\left(2\pi.t\right)\). Where: at \(t=0\), \(x=8\) and \(y=0\) then what is the nature of the path of the particle?
