Unit 4 Summary

Unit 3 Summary

A) In this unit I learned about...

• Rotational & Tangential Velocity
• Rotational Inertia
• Conservation of Angular Momentum
• Torque
• Center of Mass/Gravity
• Centripetal & Centrifugal forces

Rotational & Tangential Velocity

Rotational and tangential velocity go hand in hand when we are talking about the speed/distance at which something rotates. Although, rotational and tangential velocity are two very different things. It is easiest to understand the difference between the two with an example..... 

If there are two people running a race on a track (one starts in lane 1 and the other in lane 7) who would win the race? Most of us would suspect that the person on the innermost part of the track would win... and this is correct! But do you know why? WELL, this all depends on the rotational & tangential velocity of the runners. The person on the inside has a much smaller distance to cover per lap, therefore they will have a much faster rotational velocity (meaning that they will be making full rotations at a much faster rate than the person on the outermost lane). The person on the outside could be running faster (giving them a faster tangential velocity which is their actual speed) but it will be extremely difficult for them to run fast enough to surpass the person running on the inside. 

So.... Rotational Velocity= speed of one's RPM (rotations per minute)

& .... Tangential Velocity= the speed tangential to the center of rotation at any point (actual speed)

Rotational Inertia & Angular Momentum

Rotational Inertia has to do with how much an object is willing to rotate. If something has a high amount of rotational inertia it will be less likely to spin, while an object with very little rotational inertia will be more willing to rotate. There is a major factor that determines whether or not something will have a high or low rotational inertia is where the mass is located. If the majority of the mass is near the center of rotation, the object will more fast meaning that it has less rotational inertia. If the mass is displaced further away from the center of rotation, it will rotate slower giving it a higher rotational inertia. An example of this is with a basketball and a bowling ball. The bowling ball will roll down an inclined plane faster because more of the mass is closer to the center of rotation. Angular momentum is a counterpart to rotational inertia. It is the product of rotational inertia * rotational velocity.

Torque

Torque is what causes rotation. An object needs two things to have a torque. This is a force and a lever arm. A lever arm is the distance from the axis of rotation and the force is the force that is being applied on the object in order for it to want to rotate. We have to remember the counterclockwise torque is = to clockwise torque. This means that their lever arm and force will end up being balanced. You can get a large torque from having a 1) BIG force, 2) BIG lever arm, or 3) BOTH. An example of torque is when you are trying to un-twist a bolt with a wrench. You have to exert a certain amount of force that balances out the lever arm resulting in a torque!

Center of Mass/Gravity

Center of Mass and Gravity the the topic that I had for my podcast. The short clip above will explain the difference between center of mass and gravity and give a good example of how wrestling is applied to this concept.

Centripetal & Centrifugal Forces

FIRST OF ALL, I would like to start by making if very clear that centrifugal force is not a real thing.

Now that we have covered that, I will explain centripetal force. Centripetal force is a force that attracts objects inwards (to the center). A most basic and easily visualized example of this is the earth's pull on the moon. As the moon orbits the earth, there is a certain amount of inward pull that the earth exerts on the moon. This is centripetal force. Centripetal force is also present when you make a sharp turn in a car. Centripetal force has a little something to do with our old friend inertia. A fun fact = if at any point the centripetal force disappeared, the moon would continue moving perpendicular to the force that had been pulling on it. 

B) This unit connects with our everyday lives pretty well. Every example we dealt with, (whether is was our earth and moon's forces or trying to unhinge a screw with a wrench), the event is an everyday occurrence. I think that this factor helps especially when trying to understand Unit 4 as a whole. I hope this blog post has cleared up some confusing topics for you and good luck on your next assignment regarding this information! 

Mass of a Meter Stick Challenge

Mass of a Meter Stick

Mark and I worked together to find the mass of a meter stick in class this week. The main concept one must understand in order to complete this task is torque. Torque is, by definition, a twisting force that causes rotation. When you balance a meter stick off of the edge of a table (or some sort of pivot point) with a 100g weight on the end of it, the stick should balance somewhere around 25cm. From this discovery, you can determine the mass of the portion of the stick that is on the table and off of the table. If you add them together, you will have the mass of a meter stick and subtract 100g (the weight of the added weight). I had a lot of fun in this lab and it was even MORE rewarding when Mark and I realized that we were less than 1% off from the exact weight in grams of the meter stick. I learned from this that precise numbers and accurate readings are necessary when conducting an experiment. Overall, I enjoyed this lab! 

Torque Resource Post

Torque

In the easiest of terms, "Torque" (not to be confused with 'twerk'), is a force that makes objects want to rotate. Torque is a measure of how much a force acting on an object causes that object to rotate (clockwise or counterclockwise).

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This video gives us a quick and simple understanding of torque and how it functions. It was helpful that there were multiple different instances that showed torque being used in them and that someone went over the basics once again.

Resource Blog #1

Rotational Inertia

I felt quite strongly on my understanding of Rotational Inertia and how it works in class. But, by the time the open-note-quiz came around, I noticed that I still felt unsure about my answer. Mrs. Lawrence showed us a video and a real life example of Rotational Inertia and how it works. 

 

In the short video above, a man conducts the same kind of experiment that Mrs. Lawrence did in class, but for some reason watching it again really helped the concept to stick. Concluding that the reason the wooden block gets to the end of the ramp first is because more of its mass is closer to the axis of rotation, giving it less rotational inertia, making it move faster!

Angular Momentum

Angular Momentum was another topic we spoke about in class. I think that this video, which actually features a live classroom setting and a man creating the same effect as an ice skater has when she pulls in her arms, really helps to reinforce what we have been talking about in class.

   

This teacher is very animated (much like Mrs. Lawrence) and to watch someone talk about a certain topic, Angular Momentum in this case, with such enthusiasm makes it much easier to retain information.

Unit 3 Summary - Blog Post

Unit 3 Summary

A) In this unit I learned about...

• Newton's 3rd Law / Action and Reaction Pairs
• Tug of war / horse and buggy reactions
• Forces in perpendicular directions
• Gravity and Tides
• Momentum and impulse-momentum relationships
• Conservation of Momentum

There is a lot to say about each of these topics, but I will hopefully be able to explain each one in a simplified way and make it easier to understand.

Newton's 3rd Law / Action and Reaction Pairs

Newton's 3rd Law states that, "For every action, there is an equal and opposite reaction." This means that every time a force is applied to an object, and equal and opposite force is applied to the opposite side of it. When talking about Newton's 3rd Law, you have to mention action and reaction pairs to fully understand the concept. But BE CAREFUL, a lot of people get tripped up on the difference between action/reaction pairs and simply just two forces being equal and opposite. An example easily demonstrates the difference. 

Example of an equal and opposite action/reaction pair:

A girl, weighing 5N, is standing on the earth. The earth is also pushing up on this girl with 5N of force. This, therefore, creates a net force of 0N because the girl's force cancels out the earth's force (and vice versa). This is an example of an action and reaction pair. 

Example of an equal and opposite NON-action/reaction pair:

This same girl, still weighing 5N is now standing on top of a table. The force of the girl pushing down on the earth is still the same as before, but now the force of the table must also be taken into account. The earth will now be pushing up on the girl and the table. The force will remain equal and opposite, but this reaction does not create an action/reaction pair. (The action/reaction pairs would be between the girl and the table and the table and the earth.) 

Horse and Buggy & Tug of War (another example of action/reaction pairs)

The horse and buggy reaction and a game of tug of war are both easy examples to further prove Newton's 3rd Law. 

Horse and buggy- First of all, there is the force of the horse pulling on the buggy and the buggy pulling back on the horse. This creates an action and reaction pair and the forces and both equal and opposite. Then there is the horse pushing the ground back and the ground pushing the horse forward. This is also an action & reaction pair of equal and opposite forces. The last set of action and reaction pairs is between the buggy pushing the earth forward and the earth pushing the buggy backwards. There is one thing you have to remember about the horse/ground reaction and the buggy/ground reaction. In order for the buggy to be moving (which in this case, let's say that it is), the arrows that you draw between the horse and the ground when making a diagram must be bigger than the set of arrows between the buggy and the ground.

Tug Of War- You may be surprised to know that when you are in a tug-of-war, the winner is really not determined by who is stronger, it is more so who exerts the greater force on the ground. This means that whichever side of the rope has the bigger action/reaction pair, will win the war. 

Forces in Perpendicular Directions

Forces in perpendicular directions is basically all to do with lines and vectors. We show the amount of force exerted on a object with these vectors and that is how we can tell where the most force is being applied. 

Example:

Box A is sliding down a ramp that is not so steep, while box B is sliding down a very steep ramp. You must show the force of gravity on each box (with lines that are equal in length) pulling down on the box, and then the supporting force pulling up on the box. To find out how fast the box is actually moving down the ramp, you can draw dotted lines parallel to the opposite line and then you will be able to see that the acceleration vector will be much longer in Box B sliding down the steeper ramp. 

Gravity & Tides

Gravity and tides was a very interesting topic, and probably my favorite, throughout Unit 3. I think that I liked it so much because it really made sense and was relevant to my everyday life. To understand tides, you first need to understand gravity. Gravity equals 6.67 x 10 to the negative 11th power (a very very small number) is a force that pulls an object towards it, like the earth's pull on us. Everything with mass attracts all other things to it making f ~ m. Although, as you move farther away from that object, the force becomes less and less strong making f ~ 1/m as well. The Universal Gravitational Law is F=Gm1m2/d2. 

Example:

Planet A has a mass of 8x10 to the 30th kg, and planet B with a mass of 6x10 to the 15th kg. The two planets are a distance of 4x10 to the 22nd m. What is the force between them?

To solve this problem you have to sub in the two masses multiplied by gravity, divided by and the distance (squared) and you will be able to calculate the force.

Gravity is the main reason why we have tides. To understand tides you must know why a tidal bulge occurs on opposite sides of the earth and what a Spring and a Neap tide is. 

FUN FACT: Between every high-tide and low-tide, 6 hours pass. Therefore, it takes a full 12 hours to reach another high-tide!

• Tides have to do with the earth, moon, and sun. The gravitational pull of all three of these create our tides, although the most important is the moon. The moon has a gravitational pull on the earth causing the water on the surface of the earth to actually rise and move towards the moon. The rising and falling of the water are what we call our tides. This creates a tidal bulge around the surface of the earth. The bulge will be the same size on the opposite sides of the earth. It may seem like the side closest to the moon should have a higher tide than the side farthest away from the moon, but this is not the case. The side closest to the moon rises because there is a strong force on it, but the side farther away from the moon also rises because it is so much farther away therefore with much less force acting upon it. 

• Spring Tide occurs when the gravitational pull of the moon and the sun are combined. This creates very high high-tides and very low low-tides. There can be either a full moon or a new moon during Spring tides. 
• A Neap Tide occurs when the force of the sun and the moon are perpendicular to one another, cancelling each other out. Neap tides have a much smaller difference between high and low tides. Neap tides occur during quarter moons. 

Conservation of Momentum

Any moving object has a momentum (p=mv). In every single case, the total momentum before and after an explosion or collision will be equal to each other. An example of this would be with a canon and a cannon ball. The cannon can only push the cannon ball as far as strong as the cannon ball can push back (equal and opposite). This can be expressed in the formula ∆p=ptotal before-ptotal after. We know this because momentum is conserved in this kind of reaction, making the net external impulse = 0N. BUT WAIT, what's impulse? Well, impulse is the force upon something and how long that force is applied. It is what causes and is equal to a change in momentum (∆p=m∆v). 

• Another good example to mention is the bug crashing into a windshield. You would guess at a glance that the difference in size proportions would make there be no change in momentum for the car (since it is so much bigger than the bug), however that is not the case. Something can only be pushed as hard as it can be pushed back.

• In some special cases, such as explosions where both objects are initially at rest, one object will move forward with a positive velocity while the other moves backwards with a negative velocity. It may seem as if the ptotal before and ptotal after could not possible equal each other. Although, when you add the + velocity and the - velocity, you will find that they will cancel each other out to equal zero like before the explosion. 

Momentum & Impulse-Momentum Relationships

I think that it is important that I explain a little bit more thoroughly how momentum compares to impulse in real life situations. We already know that momentum = mass x velocity, and we also know that the total change in momentum before a reaction = the final momentum - the initial momentum. Therefore, we can conclude that the ∆p will be the same regardless of how it is actually stopped. All that matters is that we know that the object goes from moving to not moving in a certain amount of time. The ∆p = J. The only difference is that the units chance from kgm/s to Ns. We learned one very important example of this in order to prepare for the test. 

Example:

Explain why someone who jumps off of a cliff into the snow would not get as badly injured (if injured at all) as someone who jumped off a cliff and landed on an icy surface. 

1. First, I would reference the p=mv formula: The person will go from moving to not moving regardless of what surface they hit. 
2. ∆p=pfinal-pinitial: The change in momentum will always be the same, regardless of what surface stops it. All that matters is that it will go from moving to not moving over a specific period of time.
3. ∆p=J: The change in p is the same as the impulse as long as you change the units. They are the same regardless of what surface brings the person to a stop.
4. J= F•∆ t: Since J remains the same, the snow will increase the time to stop. When there is more time to stop, the force will become less and less. With less force, there is less of a chance that you will get injured.

THEREFORE:

With snow: J= F • ∆ t (less injury)

Without snow/on ice: J= F • ∆ t (more injury)

One last thing to know!

In some collisions, we have created things in order to catch or succumb to an object rather than have it bounce off. This happens with a bulletproof vest for a police officer and why cars don't have rubber bumpers anymore. In both of these cases, bouncing will occur. Bouncing is not good and has actually caused more injury than it has justice for us. When there is bouncing (bullet bouncing off of vest/cars bouncing off of each other in a crash) it creates double the force. There is 2 ∆p's, 2 J's and 2 forces. This is why our bulletproof vests work the way they do and cars do not have rubber bumpers. 

B) This unit connects with our everyday lives better than any other unit we have had so far. Every example we dealt with, (whether it was pool balls hitting off of each other, hanging a picture, or getting in a car crash), the event is an everyday occurrence. I think that this factor helps especially when trying to understand Unit 3 as a whole. I hope this blog post has cleared up some confusing topics for you and good luck on your next assignment regarding this information! 

Tides

1a) The earth will experience 2 high tides and 2 low tides in one day. It takes 6 hours to go from a high-tide to a low-tide, and 12 hours to get back to the high-tide. This is all because of the moon and the sun. The moon makes one full rotation around the earth each day. This means that it is in line with the sun and the earth two times, and it is at a 90º angle to the sun two times. This placement of the moon creates our tides.

b) There is a difference in force felt by each side of the earth. The side closer to the sun will experience a much stronger force, while the side opposite from the sun will experience a much smaller force. Still, the tides will be the same on each opposing side of the earth.

c) The tides are still the same on each side of the earth even though they have different forces. At a high-tide the earths ocean are being pulled on strongly on one side, and on the other there is a much smaller pull. Therefore, one side will rise because of the strong force upon it and the other side will rise because there is little force on it which counter-acts the stronger pull.

d) A Spring tide occurs when the gradational pull of the moon and the sun are combined. This creates very high high-tides and very low low-tides. There can be either a full moon or a new moon during Spring tides. A Neap tide occurs when the sun and moon forces are perpendicular to one another, cancelling each other out. Neap tides result in a smaller difference between high-tides and low-tides. Neap tides occur during quarter moons.

2a) At roughly 7:30 on Friday evening (14th) Nassau is experiencing a low tide.

b) About a week ago (5th, 6th, 7th) Nassau would have been experiencing Spring tides because there was a full moon. Now however, Nassau is somewhere in between because there is a half moon. When it reaches a quarter, it will be experiencing Neap tides. 

Newton's 3rd Law

This youtube video on Newton's 3rd Law was really helpful for me to gain a better understanding of the concepts and ideas that we covered in class. Newton's 3rd Law states that "For every action, there is an equal and opposite reaction." The visual effects in this video were most helpful to me. Being able to actually see the action and reaction when the tennis ball hit the earth was really helpful. Every time we talk about Newton's 3rd Law, we have to remember that the earth does move when we put our own forces on it, it is just so marginal that we do not notice. Although, in this video, the ground would sink down when the ball hit it and rise up when the ball left it. The slight exaggeration helped me to gain a more confident understanding of Newton's 3rd Law.