Instead, suppose that it was fired upward at 60◦ with respect to a horizontal line. Then its horizontal component of velocity is
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Answer:
(A) 570 rad
(B) 10 s
(C) 12.5 rad/s²
Explanation:
The equations of motion for circular motions are used.
- Initial angular velocity,
- Angular acceleration,
(A)
At <em>t</em> = 2.00 s, the angular displacement, <em>θ</em>, is given by
After this time, it decelerates through an angular displacement of 440 rad.
Total angular displacement = 130 + 440 rad = 570 rad
(B)
At the time the circuit breaker tips, the angular velocity is given by
This becomes the initial angular velocity for the decelerating motion. Because it stops, the final angular velocity is 0 rad/s. The time for this part of the motion is calculated thus:
Here, (the angular displacement during deceleration)
The subscripts, <em>i</em> and <em>f</em>, on <em>ω</em> denote the initial and final angular velocities during deceleration.
This is the time for deceleration. The deceleration began at <em>t</em> = 2 s.
Hence, the wheel stops at <em>t</em> = 2 + 8 = 10 s.
(C)
The deceleration is given by
The negative sign appears because it is a deceleration.