Unit 4 Summary

I. ROTATIONAL AND TANGENTIAL VELOCITY

Tangential velocity is the speed at which an object travels along a circular path

àdepends on the object’s distance from the axis

Rotational velocity is the number of revolutions that an object makes per unit of time (RPM’s)

Tangential velocity is directly proportional to rotational speed and radial distance

So say hypothetically, you put a raisin on the outside of a record, and one closer to the middle of the record...which has the greater a. rotational velocity, and b. tangential velocity

A. The raisin on the outside has to travel faster in order to cover a larger distance than the one on the inside. They will have the same number of revolutions per minute, therefore the same rotational velocity

B. We already established that the raisin on the outside must go faster because it is traveling a longer distance in order to keep up with the raisin on the inside. Therefore, the outside raisin has the greater tangential velocity.

How do train wheels work?

Train wheels are narrow on the outside, and wide on the inside. They will have the same rotational speed (RPM’s), but different tangential speeds. This is because the wider inside has to move faster too keep up with the narrow inside, so that they will have to same RPM’s. When the wide part is resting on one of the tracks, it has a faster speed that causes the train to curve towards the middle of the track, and self correct.

II. ROTATIONAL INERTIA AND ANGULAR MOMENTUM

Watch this video to better understand rotational inertia! I would definitely click that link if I were you…

To recap, a golf ball (solid) will have less rotational inertia than a ping-pong ball (hollow). This is because the mass of the golf ball is closer to its axis of rotation

Angular momentum= rotational inertia x rotational velocity

It is also important to remember that momentum can neither be created nor destroyed

total (angular) momentum before= total (angular) momentum after

III. TORQUES AND CENTER OF MASS/GRAVITY

A torque, in essence, is a factor that causes an object to rotate. In order for a torque to be present, you must have a force and a lever arm.

àLever arm- distance from the axis of rotation to force

    Torque= force x lever arm

The center of mass is the average position of all combined masses in an object. 

àa lever arm can occur if the center of gravity is NOT above the base of support

If you are trying to make something rotate, the best way to do so is to make the lever arm larger. Similarly, if you don’t want rotation, shorten the lever arm.

When something is balanced…

The torques are equal, but forces/lever arms are different

Clockwise torque = counter clockwise torque

F x lever arm= f x lever arm

IV. CENTRIPETAL AND CENTRIFUGAL FORCES

Centripetal force is a center seeking force that causes an object to follow a curved path.

àWhen you are riding in a car and you take a sharp curve, the centripetal force causes the car to curve inwards. Due to inertia, your body will stay in the same place while the car itself turns. Essentially, the side of the car moves into you while you sit still causing you to hit the car door. This phenomenon, that you are hitting the side of your car, is called centrifugal force. However, it is just a term used to describe this experience, it is not an actual force. Be weary…

If you have ever seen a racecar track, you will notice that the track itself has an elevated slant. This can be explained with centripetal force, check out the diagram below.

Here is another example using the flying pig from class

Meter Stick Challenge

Using just a meter stick and a 100g weight, we were given the challenge to determine the mass of said meter stick.

The first thing we did was locate the balancing point on the meter stick. We did this by resting the stick on the edge of a table and determining where it balanced on its own, which was about a third of the way up the stick.

To solve, we set up an equation using the formula

 Force x lever arm= Force x lever arm

(Lever arm= distance from axis of rotation)

Note: Convert to Kg.

Use 9.8 for weight

We multiplied the weight (9.8) and lever arm (30) of one side, and set it equal to the weight and lever arm (20) of the other side

Once we got 1.47, we divided by the weight (9.8) to get the weight of the meter stick.

After we found our hypothetical answer, we weighed the meter stick, which ended up being about 146 grams. Since the two numbers are within 10 percent of each other, we know that our process was accurate.

Torques and Basketball

Have you ever wondered why basketball players stand with their legs shoulder width apart with their knees bent? Understanding torques will help us answer this question… A torque is a factor that allows an object to rotate. Torques requires both force and a lever arm. A lever arms are the distance from the axis of rotation Torque= force x lever arm When basketball players are playing ball, it is important that they stand stationary so that they won’t fall over. If they stand with their legs shoulder width apart, they are creating a larger base, and in squatting down, a lower center of gravity. These two factors reduce the chances of a torque occurring because there is no lever arm due to the low center of gravity.

Rotational Inertia and Figure Skating

As you can see in the video, the figure skater spins slower while her arms and leg are extended out, and gains speed as she pulls her limbs in closer to her torso. What causes this change?

Rotational inertia allows an object to resist changes in spinning or circular motion. The factor that affects rotational inertia is not the AMOUNT of mass of the object, but rather the DISTRIBUTION of mass and its location on the object.

That being said, when mass is closer to the axis of rotation the object will have a smaller rotational inertia (easier to move). And when mass is further from the axis of rotation, the object will have a larger inertia (harder to move).

In terms of the ice skater…

While her arms are extended out, her mass is further from the axis of rotation, thus yielding a larger inertia. With the larger rotational inertia, she will move slower. As she brings her arms and leg towards her body, she is bringing her mass closer to the axis of rotation, resulting in a smaller rotational inertia. Hence, she spins faster.

Unit 3 Summary

NEWTONS THIRD LAW: Every action has an equal and opposite reaction

Just a few posts ago, I explained Newton’s Third Law in relation to Harry Potter and the platform nine and three quarters. Thinking back to that, we know that according to the law, every action has an equal and opposite reaction, and that Harry’s cart and the platform hit with the same force. An action reaction pair is a term used to describe the relationship between two interacting objects. In this case, the reaction pair is “cart hits wall, wall hits cart”

Don’t forget that the cart will experience a greater acceleration than the wall. This is because mass and acceleration are inversely proportional (Newton’s Second Law), so the object with a larger mass (wall) will have a smaller acceleration, and the other way around.

If you have ever played a game of tug of war, you may wonder what makes one team win over the other. According to the law, we know that each team is pulling the other with an equal force. However, the team that wins is the team that exerts a greater force on the GROUND. Refer to the diagram below for details…

 

Team red and team blue pull eachother with equal and opposite forces. However, the blue team pushes the ground with more force than the red team, which causes them to pull left with more force, and win.

VECTORS: A visual tool used to add up opposing forces

Say you have a weight hanging from a string, if the weight is on one side of the string, which side has more tension?

 

The longer the tension vectors (red) the more tension that piece of the string has. So there is more tension near the weight, and less on the other side. This means that the longer side of the string with more tension (left) is more suseptable to breakage.

GRAVITATIONAL FORCE: Everything with mass attracts all other objects with mass

Depends on…

àthe mass of the objects  

àdistance between the two objects. The more distance, the less force

Below is a the equation for finding the gravitational force between two objects, and the force of gravity itself.

 

Here is how you would use the equation

Force is directly proportional to mass

Force is inverse squared to distance

Double distanceà force is a ¼ of the original

Triple distanceà force is a ¹/₉ of the original

Cut d by ½à force is 4x’s greater

Cut d by ¹/₃à force is 9x’s greater

TIDES: As stated in my previous blog post, tides are created by the differences in force on opposite sides of the earth.  Once side of the earth has a greater force, since it is closest to the moon, and the other side which is farther from the moon experiences less force. These unbalanced forces created a “bulge” or “potato” around the earth (red)

Spring tides are high tides that are higher than usual, and occur when the sun, moon, and earth are all in one line. Similarly, neap tides are lower than typical low tides, which occur when the earth and moon create a right angle.

CONSERVATION OF MOMENTUM

p=mv

∆p=p_final-p_initial

the total momentum of a system remains constant before and after a collision

àmomentum can be neither created nor destroyed

P Total Before= P Total After

Before                 After

MaVa+MbVb=Ma+b(Vab)

MOMENTUM AND IMPULSE RELATIONSHIP

Impulse: the force exerted on something by a specific time interval

j=∆p

j=fx∆t

Have you ever wondered exactly how seatbelts keep us safe? This can be answered with knowledge of momentum and impulse…

Since change in momentum equals impulse, we know that the car will stop moving  regardless of how it stops.

àthe ∆p and j are constant

with airbag                J=F∆t

without airbag            J= F ∆t

As you can see above, force and change in time are inversely proportional. The seatbelt increases the time of the impulse, and therefore decreases the force. Less force, means it is less likely for you to be injured.

Tides

Having grown up on a peninsula, it is important to know how the tides work. The moon exerts gravitational force on the earth, which creates a difference in force on opposite sides of the earth. Since one side of the earth is closer to the moon (side A), it will have a greater force. And the side furthest away from the moon (side B) is influenced less by gravitational force. These opposing forces create an imaginary “bulge” or “potato” around the earth. Sides A and B with the bulge are at high tide, and C and D at low tide. (Insert diagram here) Spring tides are when high tides are higher than average. These tides occur during a full moon, when the moon sun and earth are all in one straight line. Similarly, neap tides are unusually low tides. These occur during the half moon phase, when the moon and earth are in a line, with the sun across from it. There are four tides every in one full day. Two low tides each lasting 6 hours, and two high tides each lasting 6 hours. Watch this video of the Bay of Fundy, in Nova Scotia Canada, home to the highest tides in the world. Below is this weekend’s tide table for Halls Harbor, Nova Scotia. At 5:18 this morning, the Harbor experienced a high tide of 32.5 feet. At 11:20, the water will leave the harbor, and the low tide will reach a height of 9.8 feet. The current phase of the moon at Halls Harbor is the “Last Quarter”, which means that at this time, the tides will be their average height for this area.