Fun Side of Mechanics Day 6 By Jonathan Abbott

Review 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

Homework Check Did anyone try to make a concept map? Would anyone like to share their work? One Example:

Impulse 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 SubwayHit 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. Survive-a-Long-Fall 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:

Bicycle Bump 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

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: PE e = ½ k x 2

Elastic Potential Energy 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 translationrotation Potential heightelasticOther

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 * v 2 /r Force = mass * speed 2 / 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?