Essentials of Physics- PHYS 101
Lectures 8/9
A joke a day keeps the doctor away Sample Exam Problems Review Torques Torques and Simple Machines Centripital Force ReviewWhy would the egg laid by a cliff bird be so pointy?
Why does a drag racer look so funny?
Not them the car!
It is built extremely long in order to get the largest rotational inertia with the least mass. You can see why this is important below. Later we will discuss what causes the wheelie problem in the first place. You can also understand why the front wheels are so wimpy looking by considering their own rotational inertia.
Torques
Why is it harder to hold something at shoulder height with your arm straight than with it bent? The weight of the object certainly doesn’t depend on how close it is to your body.
That is true, but the torque does.
Torque is the rotational motion counterpart of force.
Just like a net force will change an object’s linear motion, applying a net torque will change an object’s rotational motion.
Torque is different from force in the same way that rotational inertia is different from linear inertia. Torque and rotational inertia both depend on the distance to the axis of rotation. For torque the distance between the axis of rotation and an applied force is called the lever arm.
Torque = lever arm x force
Two children can balance a seesaw when the weight of each produces an equal torque about the pivot in opposite directions (clockwise and counter clockwise). They can do this even when they have very different weights since they can adjust each lever arm (where they sit related to the pivot) to compensate for the difference in the forces they exert. How about a kid with no friends? He can still use a seesaw! (there's hope for the lonely...)
Torque and Simple MachinesYou might get a bright idea from thinking about kids on a seesaw. If a small child can balance a large child by moving farther from the pivot point (fulcrum) then you could lift the large child using a very small force if you pushed down on the seesaw far enough away from the fulcrum. Congratulations! You just invented a machine called the lever! A machine is a devise that multiplies a force and/or changes the direction of the force.
Oops, your ambitious buddy overheard you discussing your invention and has just run off to patent the lever as a way to amplify energy. He saw how easily you lifted the large child and reasons that surely the lever allowed you to increase the Potential Energy of the child by more than the amount of work you did. Are you worried that your so-called friend will make millions off your invention in this way and leave you out in the cold?
Some interesting variations on the lever are pulleys and gears. A simple pulley is just like a lever with equal lever arms for each force. In the picture below you can see how different weights can hang from connected cylinders with different sizes and balance just like a seesaw. What would happen in the picture if the smaller cylinder was reduced in size to 0.5m?
Think of all the deep questions that you can answer now that you know about Torque.
- Why is it easier to hold something over your head rather than out to your side?
- Why is it easier to walk carrying two heavy suitcases rather than just one?
- Why is the steering wheel so large on buses and trucks? (hint: They don’t have power steering.)
- Why are doorknobs always at the edge of the door opposite from the hinges?
- Why does changing gears on my bike change how much force I need to put on the pedals? (This takes some thought.)
- Oh yes, why does a dragster tend to do a wheelie?
The torque about the axle can cause either of two rotations. Either the wheels rotate about the axle or else the car rotates about the axle.
Most people prefer to have the wheels rotate, but as the torque is increased in order to get a huge acceleration at the start that can be a challenge. Although the wheels have much less rotational inertia than the car they are still very hard to accelerate because rolling forward is resisted by the linear inertia of the entire car.
Centripital Force – “And now for something completely different!”Let’s think back to our discussions of inertia. We said that an object will travel forever at the same velocity (same speed in a straight line) unless a net force acts on the object. What does this tell us about an object that is moving in a circle?
An object moving in a circle is always accelerating (changing velocity but not speed) and therefore always has a net force acting on it. This force must be directed towards the center of the circle. Any force that is directed towards a fixed center is a Centripetal ("center-seeking") Force.
If I whirl a bucket on the end of a string I am constantly pulling towards the center, supplying a centripetal force, in order to cause the bucket to move in a circular path.
Once you finally let your buddy out of the bucket (and reluctantly re-enlarge him after letting his temper cool down) you ask him what it was like in the bucket. He describes feeling very heavy during the times when you spun the bucket fast and lighter when you slowed it down.
His conclusion is that a centrifugal force was pulling him towards the bottom of the bucket. You, however, remember from your physics class that there really is no centrifugal force. The combination of his inertia and the bucket pushing him into a circular path create a situation that is almost indistinguishable from gravity for your buddy in the bucket.
For another take on centrifugal forces, think of riding in a car when the car suddenly lurches left to avoid a pedestrian. During this process your upper body and head feel as if they are pushed to the right. In reality, they lack the centripital (center-seeking) force needed to make them move left with the car. Their inertia before the car veers has them going in a straight line. Thus, you seem to feel a centrifugal (outwards) force when the car veers. This is the basis for artificial gravity.
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