Fun Side of Mechanics Day 6By Jonathan Abbott

Review• Moment of Inertia• I = Σmi ri

2 : more mass spread out = higher moment of inertia• Higher moment of inertia = harder to start spinning

• Torque• A force that changes an object’s rotation

• Angular Momentum• The bigger an object and the faster it spins, the greater its

angular momentum

Homework Check• Did anyone try to

make a concept map?

• Would anyone like to share their work?

One Example:http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Impulse• Impulse (J) is a change in momentum (p)• Impulse J = Force * Time• So which of the following cases would have the greatest

impulse?

http://www.flickr.com/photos/trinity/164606648/sizes/m/in/photostream/

Stop the Red Line Subway Hit a baseball

Then which has a greater impulse?

• A 1000 kg old car speeding up to 15 m/s starting from rest in a total time of 10 seconds.

• A 1000 kg sports car speeding up to 15 m/s starting from rest in a total time of 2 seconds.

• The change in momentum is the same.• This means the impulse must be the same for each.• Which case then has a greater net force?• The sports car has a greater net force because it has the same

impulse in less time.

Stop a car• Stopping a car takes the same impulse whether you step on

the brake hard or just gradually slow down.

• Which method of braking is better for your car? Why?• Gradually slowing down: you give yourself more time. More

time means less net force. Less net force means easier on the brakes and safer for you.

• Good drivers anticipate braking and slow down early.

What is the purpose of a Helmet?• Helmets keep you safer. But how?• As your head collides with the ground, the

helmet gives you more time for the collision. More time = less force.

• Less Force = less damage

I should have worn a helmet…

Field Trip: How to survive a fall• We will go to this site to

explore how what we are talking about impulse applies to this topic.

• http://www.wikihow.com/Survive-a-Long-Fall

What about these?• ‘Hard’ vs ‘Soft’ surface• Airbags• Seatbelts• Dismounting from a giraffe• Jumping on a bed (so much

fun, I know)• Contact Juggling Balls• Hitting a baseball and

‘following through’• Dropping an egg on a hard

surface• Car crash: crushed

• Woodchips• Springs• Shoes• Sandpits• Glass cases (with padding)• Styrofoam Chips• Bubble Wrap• Track (as in track and field)• Basketball gym floors• Professional Clubs

Calculate the total impulse:

0 1 2 3 40

2

4

6

8

10

12

14

Impulse

Time (in seconds)

Forc

e (in

New

tons

)

0 1 2 3 40

0.5

1

1.5

2

Impulse

Time (in seconds)

Forc

e (in

New

tons

)

0 1 2 3 40

0.20.40.60.8

11.2

Impulse

Time (in seconds)

Forc

e (in

New

tons

)

Bicycle BumpWhy might larger tires be better for going over bumps?

More time = less force

Less force = less likely to fly up

Less likely to fly up/ back = less kinetic energy wasted

Springs!• As you compress or stretch a string from

its relaxed length, it exerts a force to try to go back.

• This force is proportional to distance you stretch/compress the string and also depends on the spring constant

• F = - k x• Force = - spring constant * distance

stretched

More about Springs• Similar to a spring is a rubber band.• Since when you release a stretched

rubber band or a compressed spring, what type of energy must be stored in springs?• Elastic Potential Energy

• The Elastic Potential Energy is:• PEe = ½ k x2

Elastic Potential Energy• The Elastic Potential Energy is:• PEe = ½ k x2

• How much does the elastic potential go up if I stretch a spring or a rubber band twice as far as it was previously?• It now has four times as much energy.

Kinetic

translation

rotation

Potential

height

elastic

Other

Spring Constant Lab!• Or we could call it rubber band constant lab…

Mass on a Spring• This creates simple harmonic motion, which is the case when

something oscillates. You can get simply harmonic motion with many things besides springs:

Uniform Circular Motion• Uniform Circular Motion is when an object sweeps out a

trajectory in a perfect circle. This is important because we can calculate the force needed to make this path easily.

• Force = m * v2 /r• Force = mass * speed2 / radius of the circle.• This force is ‘radially inwards’

Uniform Circular Motion• A small object spins around a ring at a constant speed.• Which way is the acceleration and force at point 3?• Which way is the acceleration and force at point 2?

Centripetal Force• We call this force that causes circular motion the centripetal

force.• ‘Centripetal’ means center seeking• Why might the rollercoaster passengers not fall out during the

loop shown below? [Hint: draw a free body diagram]

Centripetal Forces Example• Conceptual Question: Why are roads banked?