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Rookie
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Respect (85%):
Date Posted: 2/8/2008 8:35:09 PM  Status: Live
Need some help please!
Course Textbook Chapter Problem
General Physics Physics: Third Edition 7 60
Question Details:
A particle initially  at rest accelerates uniformly in a circular path at a rate of 1.5 rad/s2 for 4.0 s. The circle has a radius of 30 cm. What are a) the magnitude of the tangential  acceleration during this time and b) the tangential speed at the end of this time? I especially need help answering the second part.

Answers:

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Oracle
Karma Points: 10,131
(CSU Long Beach)
Date Posted: 2/8/2008 9:09:19 PM  Status: Live
Asker's Rating: Lifesaver   
Response:
josaka2u's Comment:
Thanks for making it clear and simple, though I'm not sure whose answer is right for part b
I rarely give answers.  I try to provide solutions.

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Expert
Karma Points: 1,391
Date Posted: 2/8/2008 9:20:00 PM  Status: Live
Asker's Rating: Somewhat Helpful   
Response:
The position components are given as
Px = r*cos(ωt),
Py = r*sin(ωt)

Since the particle travels in a fixed circular path, then the position always has the magnitude r at some angle θ. The magnitude is calculated by,

 P = √(Px2+Py2)

By taking the derivative of the position function we get the velocity function.

vx = dx/dt = -r*ω*sin(ωt)
vy = dy/dt = r*ω*cos(ωt)

Thus the speed is a constant equal to ω*r = 1.5*0.3 = 0.45 rad/s

By taking the derivative of the velocity function we get the acceleration function.

ax = d(vx)/dt = -r*ω2*cos(ωt)
ay = d(vy)/dt = -r*ω2*sin(ωt)

And the magnitude of the acceleration is ω2*r = 1.52*0.3=0.675 rad/s2
josaka2u's Comment:
Thanks for the help, though not sure of part B
If you have any questions, PM me. I hope this helps!!!



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