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Principle of Physics course includes many basic theories and concepts we study in throughout Physics. Other title of the course is Core Physics. Keywords in here are: Rotational Inertia, Linear Motion, Rotational Inertia, Conservation of Angular Momentum, Angular Momentum, Riding a Bike, Moment of Inertia
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Newton’s 2
nd^ law: F = ma
Rewrite for Rotational Motion
= m
But, should we really use m (mass)? 3)^
In Linear motion,a)^
Mass = measure of inertia b)^
Mass = resistance to change in motion
4)^
In Rotational motion, mass and how far from center (r) determine inertiaa)^
Rotational Inertia = Moment of Inertia = resistance to change inrotational motion = I b)^
I = mr
2 (Units = kg x m
2 ) for a point mass rotating around center
I depends on shape for solid objects 6)^
I replaces m for rotational motion ^
is Newton’s 2
nd^ Law
for Rotational Motion
B.^
Example Calculation: Merry-go-round I^ M^
= 800 kgm
2 , r = 2 m, 40 kg child at edge
required to cause
= 0.05 rad/s
2
2
2
2
2
C M T^
2 2
2
2
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Example Calculation: I
(arms out) = 1.2 kgm 1
(arms in) = 0.5 kgm 2
2
w^1
= 1 rev/s
w^2
Demo: student on a rotating chair 6)^
Other Examples of Conservation of Angular Momentum
2 2 1 1 2 1
2 2
(^112)
2
Kepler’s 2
nd^ Law: equal areas in equal times
L = mvr
v r ω rω v^
mvr v r ) (mr Iω L^
2
2
mv
r^11
= mv
r^22
Direction of
and L
p^ is a vector with the same direction as
v
L^ is a vector with the direction determined by
Right-hand rule establishes direction of
and
Riding a Bike ^
^ is applied to wheel to make it turn 2)^
L^ is horizontal for the motion of the turning wheel 3)^
To tip over the bike,
must be changed by another torque
That torque will be gravity working on C.O.M. of the rider/bikea)^
Axis of rotation is the line on the ground of bike’s path b)^
When upright the force is in line with the axis, so
^ = 0 (l = 0)
c)^
Conservation of momentum keeps the bike balanced d)^
When tilted,
is forward or back along the road axis
i.^
Standing still, bike falls over ii.^
Moving,
bike changes direction
iii.
Turn the wheel slightly to compensate and you stay up
e)^
Angular momentum of a moving bike makes it easier to balance
