Centripetal Force and Gravity 4/27/07
Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m.
Dec 21, 2015
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Centripetal Force and Gravity
4/27/07
Recap
= sr
= t
= t
s = r
vT = r
aT = r
ac =v2
r
ac = r2
Fc = mac = m v2
r
Fc = mac = mr2
= 2T
Recap (UCM)Uniform Circular Motion
UCM means that is constantWhich means that… = 0aT = 0|vT| = constant
BUT… vT is not constant because the direction changes
UCM
UCM
FSB
UCM
FSB
UCM
FSB
FSB
UCM
FSB
FSB
UCM
FSB
FSBFSB
UCM
FSB
FSBFSB
UCM
FSB
FSBFSB
FSB
Vertical UCM
Vertical UCM
FSB
Vertical UCM
FSB
mg
What’s keeping the ball pinned up against the top?
Vertical UCM
FSB
mg
What’s keeping the ball pinned up against the top?
Inertia
Vertical UCM
FSB
mg
Fc = F = FSB + mg
Fc is the sum of the inward forces on the ball.
Fc
Vertical UCM
FSB
mg
Fc = F = FSB + mg
Fc is the sum of the inward forces on the ball.
Fc
Fc = mr2 = m v2
r
Vertical UCM
FSB
mg
Fc = F = FSB + mg
Fc is the sum of the inward forces on the ball.
Fc
m = FSB + mg
Fc = mr2 = m v2
r
v2
r
Vertical UCM
Vertical UCM
FSB
mg
Fc is the sum of the inward forces on the ball.
Vertical UCM
FSB
mg
Fc is the sum of the inward forces on the ball.
Fc = F = …
Vertical UCM
FSB
mg
Fc is the sum of the inward forces on the ball.
Fc = F = FSB
Vertical UCM
Vertical UCM
FSB
Vertical UCM
FSB
mg
Vertical UCM
FSB
mg
Fc is the sum of the inward forces on the ball.
Fc = F =
Vertical UCM
FSB
mg
Fc is the sum of the inward forces on the ball.
Fc = F = FSB
Vertical UCM
FSB
mg
Fc is the sum of the inward forces on the ball.
Fc = F = FSB - mg
Vertical UCM
FSB
mg
Fc is the sum of the inward forces on the ball.
Fc = F = FSB - mg
Fc = mr2 = m v2
r
m = FSB - mgv2
r
Vertical UCM
Is the force of the string on the ball greater at the top or at the bottom?
Vertical UCM
FSB
mg
FSB
mgIs the force of the string on the ball greater at the top or at the bottom?
Vertical UCM
What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?
Vertical UCM
What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?
Happens when Fc just counters mg (I.e. FSB = 0)
Vertical UCM
What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?
m = mgv2
r
Happens when Fc just counters mg (I.e. FSB = 0)
Vertical UCM
What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?
m = mgv2
r
Happens when Fc just counters mg (I.e. FSB = 0)
= gv2
r
Vertical UCM
What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?
m = mgv2
r
Happens when Fc just counters mg (I.e. FSB = 0)
= gv2
r v2 = rg
Vertical UCM
What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?
m = mgv2
r
Happens when Fc just counters mg (I.e. FSB = 0)
= gv2
r v2 = rg
v = rg
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