Torque causes rotation. It is equal to force multiplied by lever arm [torque=force X lever arm]. The farther the lever arm is from the axis of rotation, the less force is required for an object to rotate. A paddle is required in order to kayak. One of the key points of this paddle, is how you hold it. The farther apart you place your arms, the easier it will be to paddle because the lever arm will be increased and the force required to move the paddle will be much less than if you were to hold the paddle with your arms close together. Although your rotational inertia would decrease because you would be holding the paddle closer towards its axis of rotation, the lever arm would be decreased therefore the force required to move the kayak would increase.
This
unit was particularly interesting because the physics we learned seemed to
relate to ever day activities even more than before.There are three main topics we learned about this unit;
rotational and tangential velocity, rotational inertia, the conservation of
angular momentum, torque, center of mass/gravity, and centripetal and
centrifugal forces.
Rotational
velocity is the number of complete rotations per time unit. Tangential velocity
can also be called linear speed because it is something moving a long a
circular path. The direction of motion is tangent to the circumference.
Tangential speed depends on the distance from the axis of rotation. Take a
merry-go round for instance, the closer you are to the middle the slower you
are going whereas on the outside you feel as though you are going much faster.
This is because the people on the outside are farther from the axis of
rotation. Everyone has the same rotational speed. Their rotational speed is
dependant upon the number of spins the platform of the merry-go round has per
time unit.
Another example is a track race. If
everyone started in an exact straight line, the race would be unfair because
the people on the outside would have to have a greater speed to keep up with
the people closer to the axis of rotation who would not need to go as fast. The
runners on the outside would have a greater tangential velocity than the
runners on the inside. Each runner has his or her own rotational speed
depending on the speed in which they are going.
Have you ever seen a car with tires
much too big for its frame? Well these people most likely get speeding tickets
frequently if they are not careful. A speedometer is accustomed to a specific
size of tires, therefore when you get larger tires than the speedometer is
accustomed to the car might read 40mph but you are really going 60mph. Although
your rotational speed decreases, your tangential speed increases and you are
covering a greater distance in a smaller amount of time because your wheels are
larger.
The last example we learned a lot
about is the wheels of a train. The wheels are designed with the wider parts in
the middle rather than the outside. The wider parts are in the middle because
the wider parts will allow the wheels to turn and go straight. The smaller
parts of the wheel will want to turn and the larger parts will direct the
wheels to remain on the tracks. In this scenario the left diameter on the track
is smaller than the right therefore it will move slower and the right will move
faster causing the wheel to curve inward. If it shifts too far where the larger
diameter is on the left, it will move faster causing the train to curve in the
opposite way, it is a method of self-correction.
Moving on to rotational inertia;
Inertia is the property of an object to resist change in motion dependant upon
the mass. Rotational inertia is the property of an object to resist changes in
the spin of an object. It is dependant upon, not the mass of each object, but
where the mass is located on that object, how it is distributed. It involves the distribution of mass and
how far away it is from the axis of rotation. If an object has a small amount
of rotational inertia, it is easier to spin compared to an object with a large
amount of rotational inertia, which is very difficult to spin.
Rotational inertia explains why
runners bend their legs instead of keeping them straight. By bending their
legs, their mass is closer to the axis of rotation lowering the rotational
inertia.
This can also explain how an ice
skater spins. When the ice skater has their leg and arms spread out and
spinning, their rotational inertia is much greater because her limbs are
farther away from his/her axis of rotation, therefore the ice skater is
spinning very slowly. However, if an ice skater brings in his/her arms and
legs, her rotational inertia decreases because she is bringing her mass closer
to her axis of rotation.
The conservation of angular and
rotational momentum is basically the same concept as the conservation of
momentum. Angular momentum is made up of two key factors: rotational inertia
and rotational velocity.Angular
momentum before equals the angular momentum just as the total momentum before
equals the total momentum after.
Conservation of Angular Momentum:
Rotational inertia X Rotational
Velocity (before) = Rotational inertia X Rotational Velocity (after)
Here’s an example of the ice skater
with angular momentum;
RI X rv (before) = ri X RV (after)
In this example, the ice skater started out with a large
rotational inertia (because she had her mass far from her axis of rotation)
therefore she had a small rotational velocity. Then, she had a small rotational
inertia (because she brought in her mass closer to her axis of rotation) and
had a large rotational velocity. We know this is true because of the conservation
of angular momentum, which informs us that the momentum before will always end
up equaling the momentum after.
Torque
is what causes an object to rotate. It equals the force of an object multiplied
by its lever arm (which is the distance from an object of rotation). If an
object has a large torque, it will have a large torque.A torque is the rotational counterpart
of force. Force changes the motion of objects whereas torque changes the
rotation. Just like rotational inertia, torque involves the distance from the
axis of rotation. This distance with torque is known as the lever arm.
In
this example, the ball on the left is hollow, therefore it a smaller force than
the ball on the right who has a larger force and although the both the ball on
the left side of the seesaw and the ball on the right side of the seesaw have
equal lever arms, the ball on the right has a greater torque because it has a
larger force therefore it has a larger torque.
However,
in this image notice that the lever arm on the left is larger than the lever on
the right. Therefore, the small force and large lever arm on the left balance
out the large force and small lever arm on the right. The lever arm on the left
was increased by simply having a greater distance from the axis of rotation.
This
is also common when dealing with bolts and wrenches. If there is a tight bolt,
you would want to have a wrench with a large lever arm because by just creating
a greater distance from the axis of rotation the force required to turn the
object will decrease and the amount of torque will be greater.
The
center of gravity is a term commonly used to express the center of mass. The
center of gravity is the average position of weight distribution. Center of
mass and center of gravity refer to the same point of an object. The center of
gravity must be above the base of support. When the center of gravity is
outside the base of support a torque happens. The center of gravity lies
directly beneath the point of suspension. The center of mass of an object may
be a point where no mass exist.
An
example where we see the center of gravity is the Leaning Tower of Pisa which
has the center of gravity lying above its base of the support therefore the
tower does no fall over. An object with a wide base and a lower center of
gravity is more stable.
A
centripetal force is a center seeking force. A centrifugal force is a center
fleeing force, however, it is a fictitious force. Think about a car going
around a turn. The friction between the tires and the road provides the
centripetal force that holds the car in a curved path. However if the friction
is not great enough, the car will skid off the road.
However,
inside this rotational system there seems to be an outward force. This outward
force is the centrifugal force. An example that might be able to explain this
more easily would be if you were a passenger of the car that was rounding the
turn. The car is turning left and you move outward to the right, technically
this was not because of a centrifugal force, it was because there wasn’t a centripetal
force to keep you in a circular motion.
This
unit was surprisingly difficult for me. The concept I struggled with the most
was torque. I was confused by the difference between torque and rotational
inertia. However, after going into conference period, I realized I needed to re
watch the torque video. In doing this, I mastered the concept and I examples in
the book involving torque.
My
problem skills throughout this unit progressively increased. At first, I
struggled with going into depth with each of the concepts presented to us. I
didn’t realize that I wasn’t going into enough depth until I began struggling
with torque. I realized I needed to be able to relate each of these concepts to
one another. So, I reviewed my notes from the previous videos and tried to find
any gaps I didn’t understand. To clarify my confusion on specific example, I
discovered that the book is actually really helpful. I think that was my key
discovery in my problem solving skills this unit (the book). My homework effort
this unit was very high and I didn’t miss an assignment and each assignment I completed
I didn’t think was just busy work, it was helpful when looking back and
studying it. Although I had a high effort in homework this unit, I need to work
on my participation in class. I am always focused in class, yet I don’t raise
my hand enough to ask questions or to answer questions. I think this could
really help me with clarifying concepts for me.
Our
podcast was a little frustrating because our group had a hard time coming up
with what to say, however, the product ended up as a really great study tool.
My original plan for solving this challenge problem worked,
however, it was much more complicated than it needed to be. We decided we would
just come up with a plan along the way. Naeem and I constructed a seesaw
instead of a countertop like the rest of the class. We rested the meter stick
on a book with the weight on one end and balanced the stick so that it appeared
horizontal. When doing this it was apparent that the side with the weight on it
had a larger lever arm than the side with the other weight. This is when we
took the formulas about torque and put them to use. The original formulas used:
t=t
t=force X leverarm
force X leverarm= force X leverarm
w=mg
clockwise torque= counter clockwise torque
After taking measurements we knew that the meter stick was
100cm. The side with the weight had a lever arm of 28cm and the side with the
meter stick balanced on it had a lever arm of 22cm. We also knew that the side
with weight had a force of 98. This is because the force on it was the force of
gravity and converting that to Newton’s it would be 98.
28
X 98= 22 X F
2744=22F
F=124.727N
The force of this really wasn’t far off yet this process
became a lot more complicated than it needed to be when the see-saw was made.
So, we followed the common method used by the class even though we got similar
answers either way. In the correct process we balanced the stick and the mass
off a tabletop. It took out the variable of the extra meter stick and we also
got different numbers. However the lever arms ended up in the same proportion
(the side with the weight had a larger lever arm than the other side). Another
thing that changed in this were the decimal points. We realized that last time
we had moved the decimal points of the force of gravity had been moved to the right
instead of the right so it actually should have been .98 rather than 98.
You don't need to watch the whole video if you have a full understanding of the basics behind torque. This source really helped me with a better understand behind torque. I liked the examples used to explain it. Although we went over the wrench example in class, it helped to have other examples with similar explanations too.
After completing homework assignments, lessons from class, and watching this video, this is my understanding of torque; Similar to a force, which is a push or pull, torque is almost as simple, it is a twist to an object. Speaking mathematically, torque is forceX the lever arm. Torque is mainly effected by these two factors (the force and the lever arm).
You can stop watching at about 1:50.
In this track race, everyone started at different distances. The people who start on the outside, are placed further ahead because they are farther from the center, therefore, they would be at a disadvantage if they started in a straight horizontal line at the start, the people would need to move faster than those people closer to the inner part of the track. The tangential speed is the distance covered per line. This is also known as linear speed. If the racers were to all start in the same line, the runner on the outside would have a faster tangential speed than the racers on the inner part of the track. The rotational speed also plays a key factor in races. Rotational speed is speed measured depending on the number of rotations per time. Therefore, the racers RPM depends on their personal speed not on their distance.
The fundamentals of running comes from physics too. All runners bend their legs when they run because they are moving their legs closer to their axis of rotation (their hips). We know this is important from the property of rotational inertia. Rotational inertia is the property of an object to resist changes in spin or rotation. It is not based upon the mass of an object, rather where that mass is located or how it is distributed (how far it is from the axis of rotation). Therefore, runners bring their mass closer to the axis of rotation to lower their rotational inertia. The farther away from the axis of rotation, the higher rotational inertia an object has.
