1) In 9.5s, a fisherman winds 2.6m of fishing line onto a reel whose r is 3cm. T
ID: 1273904 • Letter: 1
Question
1) In 9.5s, a fisherman winds 2.6m of fishing line onto a reel whose r is 3cm. The line is being reeled at a constant speed. Determine the angular speed of the reel:
2) A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from 3 to 5 revs/s while rotating through ½ of a rev. How much time does this maneuver take?:
3) During a tennis serve, a racket is given an angular acceleration of magnitude 160 rad/s2. At the top of the serve, the racket has an angular speed of 14 rad/s. If the distance between the top of the rack and the shoulder is 1.5m, find the magnitude of the total acceleration of the top of the racket:
Explanation / Answer
Number 1)
The circumference of the reel = 2pi(.03) = .1885 m
For 2.6 m of line... (2.6/.1885) = 13.8 circumferences
13.8(2pi) = 86.7 rads
w = rad/t = 86.7/9.5 = 9.12 rad/s
Number 2)
Apply (distance) = (.5)(wf + wo)(t)
.5 = (.5)(3 + 5)t
t = .125 sec
Number 3)
ac = w2r = (14)2(1.5) = 294 m/s2
a = (alpha)r = (160)(1.5) = 240 m/s2
Total acceleration = sqrt [(240)2 + (294)2]
Total acceleration = 380 m/s2
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