10.7.6 Many telescopes are housed in observatory domes, and a slit in the dome i

Question

10.7.6 Many telescopes are housed in observatory domes, and a slit in the dome is opened to allow the telescope to see the sky. The dome has to be rotated so that the slit lines up with the telescope. In one observatory, there is a motor which causes the dome to rotate counterclockwise at 0.0800 rad/s. When the motor is shut off, the dome continues to rotate, but with an angular acceleration of -0.0400 rad/s2 until the angular velocity is zero. The dome is currently rotating, and the telescope is pointed at an angle of positive 1.30 radians from north. At what angle from north should the slit be located when you shut off the motor, so that the slit lines up exactly with the telescope when the dome stops moving? (b) How long does it take for the dome to stop after the motor is shut off?

Explanation / Answer

(t)=0+t=0.08-0.04t=0 -> t=2[sec]

(t)=0+0t+0.5t2=1.3|t=2 -> 0=1.3-0.08*2+0.5*0.04*4=1.22[rad]

so:

(a)1.22[rad]

(b)2[sec]

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