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## Physics 218 Lecture 19

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### Physics 218 Lecture 19 Dr. David Toback – PowerPoint PPT presentation

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Title: Physics 218 Lecture 19

1
Physics 218Lecture 19
• Dr. David Toback

2
Schedule Changes
• Please see the handout for schedule changes
• New Exam 3 Date
• Exam 3
• Tuesday Nov. 26th

3
Angular Quantities
• Last time
• Position ? Angle q
• Velocity ? Angular Velocity w
• Acceleration ? Angular Acceleration a
• This time move forward on the others
• Force
• Mass
• Momentum
• Energy

4
(No Transcript)
5
Angular Velocity and Acceleration
• Are w and a vectors?
• w and a clearly have magnitude
• Do they have direction?

6
Right-Hand Rule
• Yes!
• Define the direction to point along the axis of
rotation
• Right-hand Rule
• This is true for Q, w and a

7
Angular Quantities
• Position ? Angle q
• Velocity ? Angular Velocity w
• Acceleration ? Angular Acceleration a
• Moving forward
• Force
• Mass
• Momentum
• Energy

8
Torque
• Torque is the analogue of Force
• Take into account the perpendicular distance from
axis
• Same force further from axis leads to more Torque

9
Slamming a door
• We know this from experience
• If we try to slam a door really hard, we grab it
at the end
• If we try to push in the middle, we arent able
to make it slam nearly as hard.

10
Torque Continued
• What if we change the angle at which the Force is
applied?
• What is the Effective Radius?

11
Slamming a door
• We know this also from experience
• If we try to slam a door really hard, we grab it
at the end and throw perpendicular to the
hinges
• If we try to pushing towards the hinges, the door
wont even slam.

12
Torque
• Torque is our slamming ability
• Write Torque as t
• t RFsinq
• (Well get to the real definition soon enough)

13
Torque and Force
• Torque problems are like Force problems
• Sum up all the Torques to find the total torque
• Is torque a vector?

14
Example Composite Wheel
• Two forces, F1 and F2, act on different radii of
a wheel, R1 and R2, at different angles Q1 and
Q2. Q1 is a right angle.
• If the axis isnt fixed, what happens?
• If the axis is fixed, what is the net Torque on
the wheel?

F2
Q2
Q1
F1
15
Angular Quantities
• Position ? Angle q
• Velocity ? Angular Velocity w
• Acceleration ? Angular Acceleration a
• Moving forward
• Force ? Torque t
• Mass
• Momentum
• Energy

16
Analogue of Mass
• The analogue of Mass is called Inertia
• Example for a ball of mass m moving in a circle
around a point
• What about lots of points? For example a Wheel.

17
Torque and Moment of Inertia
• Force vs. Torque
• Fma ?t Ia
• Mass vs. Moment of Inertia
• mass ? I SmR2

18
Two weights on a bar
Find the moment of inertia for the two different
Axes
middle
A
B
19
Spherical Heavy Pulley
• A heavy pulley, with radius R, starts at rest. We
pull on an attached rope with a constant force
FT. It accelerates to final angular speed w in
time t.
• What is the moment of Inertia?

R
20
Less Spherical Heavy Pulley
• A heavy pulley, with radius R, starts at rest. We
pull on an attached rope with constant force FT.
It accelerates to final angular speed w in time
t.
• A better estimate takes into account that there
is friction in the system. This gives a torque
(due to the axel) well call this tfric.
• What is this better estimate of the moment of
Inertia?

R
21
Pulley and Bucket
• A heavy pulley, with radius R, and known moment
of inertia I starts at rest. We attach it to a
bucket with mass m. The friction torque is tfric.
• Find the angular acceleration a

22
Rotating Rod
• A uniform rod of mass m, length l, and moment of
inertia I ml2/3 rotates around a pivot. It is
held horizontally and released.
• Find the angular acceleration a and the linear
acceleration a at the end. Where, along the rod,
is a g?

23
Next Time
• The rest of Chapter 10
• More on angular Stuff
• Angular Momentum
• Energy
• Next lecture will be the last topics on Exam 3.
• NEW EXAM DATE FOR Exam 3!!! Now Tuesday Nov 26th

24
Moments of Inertia