- #1
jumbogala
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EDIT: I meant radial in the title.
A ball is going around in a circle of radius 4 m.
It goes with a constant angular velocity of (13 rad/s)[tex]\hat{k}[/tex] for 0.5 s. After that, it takes 4 s to come to a complete stop.
Find the radial component of the ball's acceleration at 2 s.
My book says that to use the formula ar= w2r. However, w is changing, so I don't see how I can use that!
The only thing I can think of is to find the angular acceleration:
[tex]\alpha[/tex] = w0 + [tex]\alpha[/tex]0(t)
0 = (13 rad/s) + [tex]\alpha[/tex]0(4 s). Solving for [tex]\alpha[/tex] gives -3.25 rad/s2[tex]\hat{k}[/tex]
Then I use another formula to find the angular velocity at 2 s:
wfinal = winitial + [tex]\alpha[/tex](t)
wf = (13 rad/s) + (-3.25 rad/s2)(2 s)
wf = 6.5 rad/s [tex]\hat{k}[/tex]
Then use that first formula:
ar = (6.5 rad/s)2(4 m)
ar = (169 rad/sm)[tex]\hat{k}[/tex]
Are those units correct? Really the formula for ar = dVt / dt, but is what I did ok?
Also, as an aside, the TANGENTIAL part of the angular acceleration would stay the same all the time, right? If I calculated it at 1 s, 2s, ... 4.3 s, it would not change?
Homework Statement
A ball is going around in a circle of radius 4 m.
It goes with a constant angular velocity of (13 rad/s)[tex]\hat{k}[/tex] for 0.5 s. After that, it takes 4 s to come to a complete stop.
Find the radial component of the ball's acceleration at 2 s.
Homework Equations
The Attempt at a Solution
My book says that to use the formula ar= w2r. However, w is changing, so I don't see how I can use that!
The only thing I can think of is to find the angular acceleration:
[tex]\alpha[/tex] = w0 + [tex]\alpha[/tex]0(t)
0 = (13 rad/s) + [tex]\alpha[/tex]0(4 s). Solving for [tex]\alpha[/tex] gives -3.25 rad/s2[tex]\hat{k}[/tex]
Then I use another formula to find the angular velocity at 2 s:
wfinal = winitial + [tex]\alpha[/tex](t)
wf = (13 rad/s) + (-3.25 rad/s2)(2 s)
wf = 6.5 rad/s [tex]\hat{k}[/tex]
Then use that first formula:
ar = (6.5 rad/s)2(4 m)
ar = (169 rad/sm)[tex]\hat{k}[/tex]
Are those units correct? Really the formula for ar = dVt / dt, but is what I did ok?
Also, as an aside, the TANGENTIAL part of the angular acceleration would stay the same all the time, right? If I calculated it at 1 s, 2s, ... 4.3 s, it would not change?
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