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Mon. March 7th1 PHSX213 class Class stuff –HW6W solution should be graded by Wed. –HW7 should be published soon –Projects ?? ROTATION

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Mon. March 7th2 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 7th3 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 7th4 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 = r T F = r F T r F Axis of rotation

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Mon. March 7th5 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 7th6 Energy in rolling body demo

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Mon. March 7th7 Relating linear and angular variables a tan = r a R = v 2 /r = 2 r v = r

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Mon. March 7th8 Rotational Kinetic Energy Consider a rigid body rotating around a fixed axis with a constant angular velocity, . K = (½ m i v i 2 ) = ½ m i ( i R i ) 2 = ½ (m i R i 2 ) 2 = ½ I 2 Where I is the rotational inertia (aka moment of inertia), I ≡ (m i R i 2 ) about that axis.

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Mon. March 7th9 Rotational Inertia I ≡ (m i R i 2 ) For a continuous body of uniform density, I ≡ ∫ r 2 dm

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Mon. March 7th10 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 7th11 Rotational Inertia Demo

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Mon. March 7th12 Rot. Inertias for Common Rigid Bodies

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Mon. March 7th13 Calculating Rotational Inertias Example : Hollow cylinder

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Mon. March 7th14 Parallel Axis Theorem I about a parallel axis is given by I = I com + M h 2 (see proof on page 253) So, in this case, I = ½ M R M h 2

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Mon. March 7th15 Perpendicular Axis Theorem For plane figures (2- dimensional bodies whose thickness is nelgigible). I z = I x + I y (when the plane of the object is in the x-y plane)

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Mon. March 7th16 Newton II for rotations = I

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Mon. March 7th17 Example Spherical shell. What is the speed of the falling mass when it has fallen a height h ?

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Mon. March 7th18 Atwood Machine

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Mon. March 7th19 Next time More rotation, including angular momentum

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