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

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?

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?

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

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

Mon. March 7th6 Energy in rolling body demo

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

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.

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

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

Mon. March 7th11 Rotational Inertia Demo

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

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

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

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)

Mon. March 7th16 Newton II for rotations  = I 

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

Mon. March 7th18 Atwood Machine

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