mon. march 7th1 phsx213 class class stuff –hw6w solution should be graded by wed. –hw7 should be...
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Mon. March 7th 1
PHSX213 class
• Class stuff– HW6W solution
• should be graded by Wed.
– HW7 should be published soon
– Projects ??
• ROTATION
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Mon. March 7th 2
Check-Point 1• You are using a wrench and trying to loosen a rusty nut. Which of the arrangements shown is MOST effective in loosening the nut?
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Mon. March 7th 3
Check-Point 2
• You are using a wrench and trying to loosen a rusty nut. Which of the arrangements shown is LEAST effective in loosening the nut?
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Mon. March 7th 4
Torque
• The ability to cause angular acceleration, , is related to the applied force magnitude, applied force direction and the point of application of the force wrt the axis of rotation.
• = r F• r F sin = rT F = r FT
r
F
Axis of rotation
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Mon. March 7th 5
Rotational inertia (aka moment of inertia) is :
A. the rotational equivalent of mass.B. the point at which all forces appear to act.C. the time at which inertia occurs.D. an alternative term for moment arm.
Reading Quiz
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Mon. March 7th 6
Energy in rolling body demo
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Mon. March 7th 7
Relating linear and angular variables
• atan = r
• aR = v2/r = 2 r
• v = r
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Mon. March 7th 8
Rotational Kinetic Energy
• Consider a rigid body rotating around a fixed axis with a constant angular velocity, .
• K = (½ mi vi2 ) = ½ mi (i Ri)2
• = ½ (mi Ri2) 2
• = ½ I 2
• Where I is the rotational inertia (aka moment
of inertia), I ≡ (mi Ri2) about that axis.
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Mon. March 7th 9
Rotational Inertia
• I ≡ (mi Ri2)
• For a continuous body of uniform density, I ≡ ∫ r2 dm
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Mon. March 7th 10
Check-Point 3
• An ice-skater spins about a vertical axis through her body with her arms held out. As she draws her arms in, her angular velocity:
• A) increases
• B) decreases
• C) remains the same
• D) need more information
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Mon. March 7th 11
Rotational Inertia Demo
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Mon. March 7th 12
Rot. Inertias for Common Rigid Bodies
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Mon. March 7th 13
Calculating Rotational Inertias
Example :
Hollow cylinder
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Mon. March 7th 14
Parallel Axis Theorem
• I about a parallel axis is given by
• I = I com + M h2 (see proof on page 253)
• So, in this case,
• I = ½ M R02 + M h2
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Mon. March 7th 15
Perpendicular Axis Theorem
• For plane figures (2-dimensional bodies whose thickness is nelgigible).
• Iz = Ix + Iy (when the plane of the object is in the x-y plane)
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Mon. March 7th 16
Newton II for rotations
= I
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Mon. March 7th 17
Example 10.67
Spherical shell.
What is the speed of the falling mass when it has fallen a height h ?
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Mon. March 7th 18
Atwood Machine
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Mon. March 7th 19
Next time
• More rotation, including angular momentum