InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A dics rotates about the central axis starting from rest and accelerates with constant angular accelertion. At one time, it is rotating at `10 rps` , `60` revoluting later, its angular speed is `15rps`. Calculate (i) angular acceleration (ii) time required to complate `60` revols (iii) the time required to reach `10 rev//sec` angular speed and (iv) number of revoluting from rest until the time the disc reaches `10rps` angular speed. |
|
Answer» Here, `omega_(0) = 10rps = 20 pi rad//s` `theta = 60 revols = 60 xx 2 pi radian` `omega = 15 rps = 15 xx 2 pi rad//s` From `omega^(2) - omega_(0)^(2) = 2 alpha theta` `alpha = (omega^(2) - omega_(0)^(2))/(2 theta) = ((30 pi)^(2) - (20 pi)^(2))/(2 xx 60 xx 2pi)` `alpha = (500 pi^(2))/(240 pi) = (25)/(12) xx 3.14 rad//s^(2)` `= 6.54 rad//s^(2)` From `omega = omega_(0) + alpha t` `t = (omega - omega_(0))/(alpha) = (30pi - 20 pi)/(6.54)` `t = (10 xx 3.14)/(6.54) = 4.8 s` (ii) In this case, `omega_(0) = 0, omega = 10 xx 2 pi rad//s` ` alpha = (omega - omega_(0))/(alpha) = (20pi - 0)/(6.54) = 9.6 s` (iv) In this time, `theta = (omega^(2) - omega_(0)^(2))/(2 alpha) = ((20pi)^(2) - 0)/(2 xx 6.54) = (400pi^(2))/(13.08)` Number of revolutions `= (theta)/(2pi) = (400pi^(2))/(2pi xx 13.08) = 48.0` |
|