By Jonathan Abbott

• Moment of Inertia
• I = Σm i r i
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

• 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 (J) is a change in momentum (p)
• Impulse J = Force * Time
• So which of the following cases would have the greatest impulse?
Stop the Red Line Subway Hit a baseball http://www.flickr.com/photos/trinity/164606648/sizes/m/in/photostream/

• 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.

• 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.

• 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…

• 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

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

14
12
10
8
6
4
2
0
0
Impulse
1,5
1
0,5
0
0
Impulse
4
1 2
Time (in seconds)
3
2
1,5
1
0,5
0
0
4
Impulse
1 2
Time (in seconds)
3
1 2 3
Time (in seconds)
4

Why 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

• 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

• 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:
• PE e
= ½ k x 2

• The Elastic Potential Energy is:
• PE e
= ½ k x 2
• 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 Potential translation height rotation elastic
Other

• Or we could call it rubber band constant lab…

• 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 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 * v 2 /r
• Force = mass * speed 2 / radius of the circle.
• This force is ‘radially inwards’

• 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?

• 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]

• Conceptual Question: Why are roads banked?