1, Module Lecture 5
Given: A 2 m long 90 N plank hangs vertically from a frictionless hinge. The plank is struck 1.5 m below the hinge by a 3 kg ball traveling at 10 m/s. The ball rebounds at 6 m/s. Required: Angular velocity of the plank.
Example: Spinning bicycle wheel I
Xu is holding the spinning bicycle wheel while standing on a platform that can rotate freely. Suddenly he flips the bicycle wheel over so it is spinning in the opposite direction. What happens? A. Platform starts rotating in direction wheel was originally rotating B. Platform starts rotating in opposite direction of original wheel rotation C. Platform stays at rest D. Platform turns only while Xu is flipping the wheel Now he moves the wheel only 90 so it is vertical. What happens ? A. Platform starts rotating in same direction and speed as before B. Platform starts rotating in same direction as before, but at a slower speed C. Platform stays at rest D. Platform turns only while Xu is flipping the wheel
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Why is linear momentum not conserved?
EF 152 Fall, 2008 Lecture 1-5
Example: Spinning bicycle wheel III
Cheryl is holding a rapidly spinning bicycle wheel so the axis is horizontal. Xu strikes the outer end of the axle with a downward hammer blow. What happens to the wheel? A. B. C. D. E. Axle tilts downward Wheel remains horizontal, but rotates to left Wheel remains horizontal, but rotates to right Nothing happens Cheryl throws the at wheel Xu
Example: Spinning bicycle wheel III
Linear Impulse
J=
z
Impulse gives change in ___________ Angular impulse gives change in ___________ Angular Impulse: x
y
y x
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Example: Spinning bicycle wheel III
Why the surprising result? A downward blow causes the wheel to rotate to the left. Linear motion Parallel force: Perpendicular force: Angular motion Parallel torque: Perpendicular torque:
General 3D Motion
Linear
F = F
net
= ma
Mass was considered concentrated at ____________ Rotation Need a _____________ point Natural choices:
cm
=
dLcm = I dt
LA = (R P ) + Lcm
A = (R Fnet ) + cm
EF 152 Fall, 2008 Lecture 1-5
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EF 152 Fall, 2008 Lecture 1-5
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Example: Dropping a ball of string
Given: String is wrapped around a uniform solid cylinder of mass M and radius R. The cylinder starts from rest. Required: Speed, acceleration, and tension in string after it has fallen a distance h.
Review: Analogies between Linear and Angular Motion
Quantity Displacement Velocity Acceleration Momentum Force Impulse Kinetic Energy Work Power Linear Motion Angular Motion
r d = r dt r r d d 2 = =2 dt dt r r dL r r = rF dt
r dr
r r dr v= r dt r r dv d 2 r a= = dt dt 2
r d
r r p = mv
r rvr L = I = r p
=
r
rr p = Ft
r r dp F= dt
rr L = t
mv 2 rr F dr
1 2
I 2 r r d
1 2
rr vF
rr
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EF 152 Fall, 2008 Lecture 1-5
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EF 152 Fall, 2008 Lecture 1-5