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Physics 218 Lecture 19

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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
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