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Physics 218Lecture 19

- Dr. David Toback

Schedule Changes

- Please see the handout for schedule changes
- New Exam 3 Date
- Exam 3
- Tuesday Nov. 26th

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

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Angular Velocity and Acceleration

- Are w and a vectors?
- w and a clearly have magnitude
- Do they have direction?

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

Angular Quantities

- Position ? Angle q
- Velocity ? Angular Velocity w
- Acceleration ? Angular Acceleration a
- Moving forward
- Force
- Mass
- Momentum
- Energy

Torque

- Torque is the analogue of Force
- Take into account the perpendicular distance from

axis - Same force further from axis leads to more Torque

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.

Torque Continued

- What if we change the angle at which the Force is

applied? - What is the Effective Radius?

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.

Torque

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

Torque and Force

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

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

Angular Quantities

- Position ? Angle q
- Velocity ? Angular Velocity w
- Acceleration ? Angular Acceleration a
- Moving forward
- Force ? Torque t
- Mass
- Momentum
- Energy

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.

Torque and Moment of Inertia

- Force vs. Torque
- Fma ?t Ia
- Mass vs. Moment of Inertia
- mass ? I SmR2

Two weights on a bar

Find the moment of inertia for the two different

Axes

middle

A

B

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

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

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

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?

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

Moments of Inertia