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F acceleration, a
angular acceleration,
m/sec2
radians/sec2
ordegrees/sec2
We’ve seen our “equations of motion”complemented by descriptions of
spinning and rotation:
Recall:
(linear) momentum: mv = constant
m/sec
(linear) momentum: I = constantradians/sec
Fgravity
The moon is always “falling”, but
- Never changes speed:
No increase inKinetic Energy!
- Never gets any closer to the earth:
No decrease inPotential Energy!
Center of mass/ center of balance
Fgrav
Fgrav
FgravFgrav
N
N
N
N
A tricycle provides a large baseand ordinarily a rider’s center of massis comfortably within its boundaries.
f
v v
f vBut a child’s inertiacan carry them tooeasily outside that
bounds on a fast turn.
Note the low center-of-mass for riders of a Big Wheel
What helps keep a bicycle steady?
This unicyle is being ridden past you to the left.By the right-hand-rule, the angular momentumof the wheel points
A. right. B. left.C. down. D. up.E. into the screen.F. out of the screen.
2
iirmIrotational mass
somewhat large since some body parts are held
out at large distances ri from the center.
now all body parts
are held in at small ri from the center.
I11 = I22
This motorcyclist is A. falling down.B. making a left turn.C. making a right turn.
W
N
f
N
f
total forcefrom road surface on motorcycle
N
f
But what about the torque gravity applies?
The total surface forces are not off-centered at allso produce no net torque of their own!
If this wheel started to tip to the left:
This would be due to a torque(applied by gravity)
By the right-hand-rule, this torque points in what direction?
A. right. B. left.C. down. D. up.E. into the screen.F. out of the screen.
A torque of course produces a change in angular momentum:
This changewill be inthe directionof the torque(out towardsyou in thispicture). '
the new angular momentum
What does this mean?
This gyroscopic precession will actually steer the wheel naturally to the left!
ballballcuecuevm vm
5500
Head-on elastic collisions:
ballcuev v
5
V
of equal masses:
What happens in a head-on collisionwith a much heavier mass?
V
V ~V
What about the (more common) glancing blow?
Remember:contact forces are NORMAL forces!
To understand what effect this has, consider bouncing a ball off the ground…
A glancing blow with the ground is like partly traveling straight down
into it and, at the same time, trying to
travel past it.
This part of its motion(the downward component of its velocity) is reversedby the collision, just like a head-on collision event.
The horizontalcomponent of its
motion is unaffected!
F. With the fingers of your right hand curled in the direction of the rotating wheel, your thumb will point out of the screen.
B. He is leaning to turn to his left.
F. out of the screen.
The direction a torque twists is defined by the same right-hand rule. When screwing inan ordinary (right-hand threaded) screw, with screw- driver in right hand, yourfingers curl in the directionyou’re twisting, and your thumbpoints in the direction you’re driving the screw (the directionof the torque).
Sure, the initial angular momentum of the spinning wheel is to the left. But the torque that’s trying to tip the wheel is rotating it so that the top of the wheel falls over to the left…a counter-clockwise twist of thetop over the bottom edge which is against the ground.
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