Post on 03-Jan-2016
Twirling a Ball on a String VerticallyTwirling a Ball on a String Vertically
gRvvgRv
mgR
vmTIfmg
R
vmT
R
vmmgT
R
vmF
topcrtopcr
net
__
22
22
or
0
x
mgT
T = 0; vcr
mgmaR
T
mgmaR T cannot be
negative, the bob will fall down!
mgmaR
If an object is moving in a circular path but at varying speeds, it must have a tangential component to its acceleration as well as the radial one.
Non-uniform Circular Motion
Sustained vertical spinning• Ever wonder what a bike
tire feels like?• At constant speed, the
centripetal acceleration is constant (v2/r), but the direction of gravity keeps changing!
• Feel heavier at bottom than at top
• This ride definitely turns your world around!
Bridges & Speed BumpsBridges & Speed Bumps
gRvN
m
NRgRv
R
vmNmg
R
vmF
Cr
net
0
2
2
The curvature of the bridge/bump and your speed determines if you are going to stay on the bump (N>0) or if you are going to bump: fly off it!
Connected BodiesConnected Bodies
Two different masses (m < M) are connected
by a string going through a tube. Predict
what will happen when you whirl the
lighter mass with constant but high speed.
Base your prediction on the CM model.
m
M1. Mass M will be falling down since it is heavier
2. Mass M will be moving up and then stop
3. Mass M will move up and then will fall down
4. It is impossible to whirl the lighter mass around
Connected Bodies - AnalysisConnected Bodies - Analysis
m
MgRv
R
vmMg
TMgR
vmT
FR
vmF
Mnet
mnet
)cos(
)cos(
0
)cos(
0
2
2
_
2
_
If the mv2/R is > Mg, the mass M will accelerate upwards. Notice, the mass m will always rotate so the string is not horizontal. It happens so T has a vertical component to cancel out the mg!
m
M
T
mgx
y