1.) Rotational and Tangential Velocity
2.) Rotational Inertia and Conservation of Angular Momentum
3,) Torque and Center of Mass/ Gravity
4.) Centripetal and Centrifugal Force
Just like in the last semester's units, I learned of numerous formulas, concepts and everyday applications. What sets this unit apart is that it was generally exciting to find things out such as why a train doesn't run off the tracks or why an ice skater goes faster when they pull their arms in. All of this and more will be answered below.
Part one: Rotational and Tangential Velocity
1.) What is tangential speed?
It is the direction of motion tangent to the circumference, the linear speed of something moving along a circular path.
2.) What are the units it's measure in?
It is measured in m/s or km/h.
3.) Does tangential speed depend on the radial distance (distance from the axis)?
Yes, yes it does.
4.) What tangential speed directly related to?
It is directly related to rotational speed.
5.) What does rotational speed involve?
It involves the number of rotations or revolutions per unit of time.
6.) What do all parts share?
They share the same rate of rotation/ number of rotations/revolutions.
7.) What unit is rotational velocity measure in?
It is measured in RPM's ( revolutions per minute).
8.) Is there speed in the center of the rotating platform?
No, there is not speed, just rotational.
9.) Keep this in mind...
Examples and Practice Problems (Some exercises from our textbook)
1.) How are train wheel designed so they stay on the track?
Train wheels are tapered with the fat/wider part on the middle, the more narrow part on the outside. All parts of the wheel gave the same rotational speed, but the wider part has a greater tangential speed. This difference causes the wheels to curve when the wider part is on the track. The wheels curve inward, setting the train in the middle when it is in the middle of the track.
2.) Look at the adorable kids on the merry-go-round. Specifically look at the girl sitting down (kid a) and the boy sitting behind her to her right (kid b). Which kid has the greater....
a.) Tangential velocity and why?
Kid B has the greater tangential because he is farther from the axis of rotation.
b.) Rotational velocity and why?
They have the same rotational velocity because their distance to the axis of rotation doesn't matter. They will have the same number of rotations around the merry go round.
2.) An automobile speedometer is configured to read speed proportional to the rotational speed of its wheels. If larger wheels, such as those of snow tires,are used, will the speedometer reading be high, low- or no different?
Lower because the bigger wheel will cover more distance per revolution and the speedometer is only accounting for the revolutions for the smaller tire.
3.) Fill in the blanks for the following....
a.) Gears work by having the same ________ velocity, but different ________ velocity.
b.) Train wheels autocorrect by having the same ________ velocity, but different ________ velocity.
Answer for a: tangential/ rotational
Answer for b: rotational/tangential
Part two- Rotational Inertia and Conservation of Angular Momentum
1.) What is rotational inertia?
The property of an object to resist changes to spin, A.K.A how much an object is willing to spin.
2.) What causes it to increase or decrease (i.e what does it depend on)?
The location of the mass in relation to the axis of rotation.
3.) What does the conservation of rotational/angular momentum mean?
It means once you start to spin you will continue to spin.
4.) What two things affect the amount of rotational/angular momentum?
The two things that affect it are rotational velocity and rotational inertia.
5.) If something has a high amount of rotational inertia, will it be more or less likely to spin?
It will be less likely to spin.
Examples and Practice Problems (Some exercises taken from our textbook)
1.) Why was the meter stick with the masses closer to center easier to rotate?
It has a small amount of rotational inertia so it is easier to rotate.
2.) Why do runners bend their legs when they run rather than keeping them outstretched?
They bend their legs because it brings their mass closer to their axis of rotation, decreasing their rotational inertia.
3.) An ice skater is spinning with his arms close to his body. Is his rotational inertia high or low? Is his rotational velocity high or low?
His rotational inertia is low. His rotational velocity is high.
4.) The same ice skater now stretches his arms outward. What happens to his rotational inertia? What can you predict will happen to his rotational velocity?
His rotational inertia is high. His rotational velocity is low.
5.) Which would win a race down a ramp - a solid steel ball or a hoop and why?
The solid steel would win the race, believe it or not. The ball would win because its mass it closer to the center versus the hoop whose mass is more concentrated toward the outside.
6.) Which would win a race down a ramp - a frozen bottle of water or an unfrozen bottle of water and why?
The frozen water bottle would win because it, like the steel ball, has it's mass concentrated in the center. On the other hand, the unfrozen water bottle's mass isn't solid and is moving around the outside of the water battle rather than remaining in the center.
7.) Why are lightweight tires preferred over lightweight frames in bicycle racing?
Hopefully you know the answer by now! However, just in case, I will write it out. The light weight tires mean you have a low rotational inertia so it will spoon easier. When you have a heavy frame the mass will be away from the axis of rotation, so it will remain in the middle A.K.A less likely to rotate.
8.) A large amount of soil is washed down from the Mississippi river to the Gulf of Mexico each year. What effect does this have on the length of the day?
The day would get longer.
Part three- Torque and Center of Mass/ Gravity
1.) What does a torque cause?
It causes rotation.
2.) What two things does torque require (i.e What is torque equal to)?
It requires a force and lever arm.
3.) What is the formula to find the torque of an object?
Torque= Force x Lever Arm
4.) What is a lever arm?
It is the distance from the axis of rotation to where the force is applied.
5.) When something is balanced, what do I know about the clockwise and counter clockwise torques?
They are equal.
6.) What are three different ways you could get a large torque?
You can increase your lever arm, force, or both.
7.) How can you have a large torque without having a large force (i.e How can a very small force cause a large torque)?
If you have a large lever arm then you only need to apply a small force to get a large torque.
8.) What is the center of mass?
The average position of an objects mass.
9.) What is the center of gravity?
The specific point on all objects that gravity acts on.
10.) What two things cause you to be more stable?
The two things that cause you to be more stable are lowering your center of gravity and widening your base of support.
11.) What will an object need to do in order to fall over?
An object will need to rotate outside of its base of support.
Examples and Practice Problems (Some exercises taken from our textbook)
1.) Why do more objects tip over when the center of gravity us not over their base of support?
This is because it creates a lever arm, which combined with force creates a torque. Torque causes rotation.
2.) Why is putting a door stop closer to the handle better than putting it close to the hinge?
By putting the door stop closer to the handle, the lever arm is lengthened which requires less force than if the lever arm was smaller.
3.) Why do wrestlers bend their knees and have their feet shoulder width apart when wrestling?
They do this to lower their center of gravity and increase their base of support. The wider base of support and lower center of gravity makes it harder to rotate outside of the base of support, in turn making them more stable.
4.) Where would you place your finger if you were trying to balance a hammer and/or a broom?
For a hammer or broom you place it near the head of the tool. You place it near the head of the top because that is where the center of gravity is. The lever arm then doesn't need to be nearly as long to equalize the counterclockwise and clockwise torques.
5.) The rock and the meter stick balance at the 25cm mark, in the picture below. The meter stick has a mass of 1kg. What must be the mass of the rock?
Answer....
6.) Is the net torque changed when a partner on a seesaw stands of hangs from her end instead of sitting? (Does the weight of the lever arm change?)
No, it does not change.
7.) Can a force produce a torque when there is no lever arm?
No, it cannot because the formula for Torque = Force x Lever Arm.
8.) Why is a long pole more beneficial to a tightrope walker if the pole droops?
It is more beneficial because it widens his base of support, making it harder for him to rotate out of it.
9.) The center of gravity of the three trucks parked on a hill are shown by the X's. Which truck(s) will tip over?
It will be the first one because when you draw a line from the red x then went diagonally, only the last two truck's lines would be over the base of support.
10.) A long tack balanced like a seesaw supports a golf ball and a more massive billiard ball with a compressed spring between the two. When the spring is released, the balls move away from each other. Does the track tip clockwise, tip counterclockwise, or remain in the balance as the balls roll outward?
It will remain balanced because the counterclockwise and clockwise torques are equal. The torques are equal because the billiard ball will have a big force, but a short lever arm, The golf ball will have a small force with a large lever arm.
11.) Why are football players less likely to be pushed over when they keep their legs shoulder width wide vs. feet together?
They are less likely to be pushed over because they have a wider base of support. When they have a wider base of support it is harder to rotate outside of it.
12.) A long stick is balanced as is shown below. What is the weight of the stick? (show work)
Part four- Centripetal and Centrifugal force
1.) What is a centripetal force?
It is a center seeking force.
2.) What is a centrifugal force?
It is a lie! This is because it is a fictitious force.
Here is an example of centripetal force to give you an idea of what that might look like..
3.) The velocity of an object is always ________ to the circle?
Answer: Tangent
4.) What force causes you to fling out when turning in a car?
It is the centripetal force.
Examples and Practice Problems (Some exercises from our textbook)
1.) What force causes the water to fling out in a salad spinner whilst spinning it? (See the video below if you are unaware of what a salad spinner is, looks like, or how it functions.) (Answer is posted below video.)
It is the absence of centripetal force on the water. This is because if there were centripetal force then the water would curve when it flew out instead of going straight. Centripetal force is the key component in something wanting to curve.
2.) Describe the force that keeps you in the car when turning: what is it, what direction does it act, and how does this work?
The force is centripetal force. It acts in the inward direction because it is a center seeking force.
3.) What direction does an object move in a circle compared to the force exerted on it that keeps it in the circle? (see picture in question number 8)
It moves tangent to the circle.
4.) Why are race track curves built at an angle?
They are built at an angle because the F weight and F support add up to create a centripetal force which keeps the driver and the car on the track.
5.) Can an object move along a curved path if no force acts on it? Explain
6.) You are on a race track and it's been snowing! The ground is covered in a thin layer of frost and friction is need for you to round the curve of the final lap! If the track is banked, friction may not be needed at all. What, then, supplies the needed centripetal force?
The F support and F weight supplies the needed centripetal force.
7.) Are satellites stationary above the earth? How do they stay close to the earth without flying into space and also not hitting the earth?
No, they're not stationary. They stay close to the earth because they're given a certain velocity, not too fast or too slow, so that the centripetal force of gravity pulls it in close to the earth.
8.) Label the centripetal force and the tangential velocity below and it's direction....
Answer....
9.) The car below is on a banked racetrack. There is a centripetal force acting on this car keeping it on the track. With labeled vectors, show where this centripetal force comes from.
Answer...
With a flying object it is similar, but with one small difference. See if you can spot the difference.....
Answer: The difference is that there is no F support. Instead of F support, there is F tension.
You made it to the end! I know that was a lot of work, but you are made better for it!
