Mon. March 7th 1

PHSX213 class

• Class stuff– HW6W solution

• should be graded by Wed.

– HW7 should be published soon

– Projects ??

• ROTATION

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?

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?

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

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

Mon. March 7th 6

Energy in rolling body demo

Mon. March 7th 7

Relating linear and angular variables

• atan = r

• aR = v2/r = 2 r

• v = r

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.

Mon. March 7th 9

Rotational Inertia

• I ≡ (mi Ri2)

• For a continuous body of uniform density, I ≡ ∫ r2 dm

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

Mon. March 7th 11

Rotational Inertia Demo

Mon. March 7th 12

Rot. Inertias for Common Rigid Bodies

Mon. March 7th 13

Calculating Rotational Inertias

Example :

Hollow cylinder

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

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)

Mon. March 7th 16

Newton II for rotations

= I

Mon. March 7th 17

Example 10.67

Spherical shell.

What is the speed of the falling mass when it has fallen a height h ?

Mon. March 7th 18

Atwood Machine

Mon. March 7th 19

Next time

• More rotation, including angular momentum