With a ramp, you said that we still do the same work, but with less force. But if work is force times distance, if force is less, shouldn't work be less as well? How is distance affect by the ramp?

When you lift an object using a ramp, the uphill force you exert on it is less than its weight but the distance you must travel along the ramp is more than if you simply lifted the object straight up. When I lifted the cart weighing 15 N straight up for 0.2 meters, I did 3 newton-meter or 3 joules of work on it. To raise the cart that same 0.2 meters upward on the ramp, I'd have to exert a 3 N force on it as I pulled it 1.0 meter along the ramp. The work I did raise the cart by pulling it along the ramp would be 3 joules again. No matter how I raise the cart to the height of 0.2 meters, I'm going to do 3 joules of work on it.

What are the three quantities of rotational motion?

Angular position specifies an object's orientation. Angular velocity specifies how that object's angular position is changing with time. Angular acceleration specifies how that object's angular velocity is changing with time.

What are Newton's three laws for rotation?

Newton's first law says that a rigid object that's free of torque will spin with constant angular velocity. The second law says that the product of an object's moment of inertia times it angular acceleration is equal to the torque causing that angular acceleration. The third law says that if you exert a torque on an object, it will exert an equal but oppositely directed torque on you.

Along with the falling egg, I was thinking about a falling dish or glass. Why when a glass falls to the floor sometimes it will break and other times in the exact same situation it won't break?

When the glass hits the floor, the floor exerts all of its force on the part of the glass that actually touches the glass. That small part of the glass accelerates upward quickly and comes to rest. The remainder of the glass isn't supported by the floor and continues downward. However the glass is pretty rigid and parts of it begin to exert forces on one another in order to stop the whole glass from traveling downward. These internal forces can be enormous and they can rip the glass apart. Glass is a remarkable material; it never dents, it only breaks. As the glass tries to come to a stop, the internal forces may bend it significantly. It will either tolerate those bends and later return to its original shape or it will tear into pieces. Which of the two will occur depends critically on the precise locations and amounts of the forces. If the forces act on a defect on the glass's surface, it will crack and tear and the glass is history. If the forces all act on strong parts of the glass, it may survive without damage.

When you exert a torque on a merry-go-round, how does it exert one on you (because for me, I have to exert a lot of torque to get it going but it doesn't feel like torque is being put back on me)?

When you spin a merry-go-round, you exert a torque on it and it exerts a torque back on you. If you were free to rotate, this torque on you would be quite apparent. Suppose that the merry-go-round was located on an ice skating rink and that you were attached to the central pivot of the merry-go-round by a strap that went around your waist. As you spun the merry-go-round clockwise, you would begin to spin counter-clockwise. In fact, because your moment of inertia is much smaller than that of the merry-go-round, you would experience a much larger angular acceleration and would end up spinning much faster than merry-go-round. The reason that you don't rotate like this after spinning a playground merry-go-round is that your feet touch the ground. As the merry-go-round exerts its torque back on you, you exert that same torque on the ground. The result is that the earth undergoes angular acceleration in the opposite direction from that of the merry-go-round. Because the earth's moment of inertia is so huge, you can't tell that it undergoes angular acceleration at all. It really does, just as the earth undergoes acceleration when you jump-you push down hard and the earth as it pushes up hard on you and you both accelerate away from one another. Since the earth is much more massive than you are, it doesn't accelerate nearly as much as you do.

What is the formula for Newton's second law of rotation?

It's torque equals moment of inertia times angular acceleration. Thus the more torque you exert on an object or the smaller its moment of inertia, the larger its angular acceleration.

Still the space shuttle: if it always falls toward the center of the earth, how does it get to outer space? If something accelerates, doesn't it go faster and thus have its speed increase?

The second question first: no, an object can accelerate without going faster. In fact, a stopping object is accelerating! If an accelerating object can speed up or slow down, it can certainly maintain a constant speed. If you swing a ball around in a circle on a string, that ball is accelerating all the time but its speed isn't changing. Now the first question: for the space shuttle to get to outer space (i.e. more than a few hundred miles above the earth), it must travel even faster than it normally does. Its usual speed keeps it traveling in a circle near the earth's surface. If it went a bit faster, its path wouldn't be bent downward as much and it would travel more in a straight line and way from the earth.

How do rubber bouncing balls work? Does the table exert more force than is applied, causing an upward acceleration?

The table never pushes up on the ball harder than the ball pushes down on the table. That would violate Newton's third law and is just not the way our universe works. As the ball strikes the table, the two objects dent. The ball dents most and has work done on its surface-the table pushes the surface inward; force times distance in the direction of that force. The ball stores this work/energy as a deformation of its elastic surface and a compression of the air inside the ball. The ball then rebounds from the table as this stored energy reemerges as kinetic energy in the ball. Throughout the bounce, the upward force that the table exerts on the ball is much larger than the ball's downward weight. As a result, the ball accelerates upward the whole time. It starts the bounce heading downward and finishes the bounce heading upward.

How since the bowling ball is moving with your body can there be no force applied on it?

When I walked across the room at a constant velocity, holding the bowling ball, I did no work on the bowling ball. The force that I was exerting the ball was straight upward, in order to balance its downward weight, and the distance that the ball traveled was horizontal in the direction I was walking. Since the force and distance traveled were at right angles to one another, I was doing no work on the ball. But I was exerting an upward force on it. Since this upward force exactly balanced gravity, the ball itself experienced exactly zero net force and didn't accelerate. Its energy never changed.

Why does a basketball bounce higher than a bowling ball?

When a ball bounces from a rigid surface, the ball's surface distorts inward and then pops back outward. During the inward motion, the ball stores energy-pushing its surface inward takes energy. During the outward motion, the ball releases that stored energy. But not all the energy invested in the ball emerges as useful work. Some of that energy is turned into thermal energy and never reappears. A properly inflated basketball returns a good fraction of the energy it receives while other balls may not. In fact, a bowling ball bounces pretty well from a hard surface such as cement. But when it hits a softer surface such as wood, the wood receives much of its energy and wastes that energy as thermal energy.

When you push up on an object, are you creating thermal energy or does that only occur when something does work on you?

When you lift a heavy object, you do work on that object. After all, you exert an upward force on it and it moves in the direction of that force. However your muscles are inefficient and you consume more food energy (calories) during the lifting process than you actually transfer to the heavy object. Whatever energy you consume that doesn't go into the object remains in you as thermal energy. Any time you tighten your muscles, whether you do work on something, it does work on you, or neither does work on the other, you end up wasting some food energy as thermal energy.

When you stand in a doorway and push your arms against the sides of it, why do your arms float upward when you step out of the doorway?

That's just a physiological effect. When you stress muscles for a long time, they become accustomed to opposing the stress and you don't feel it any more. When you the stress is removed, the muscles keep opposing the now vanished stress and, in this case, your arms "float" upward.

You said that it is impossible to overcome the speed of a falling object. However isn't it true that a skydiver who jumps second from a plane can put themselves in an aerodynamic position and gain speed on the person who jumped first? Or does this have to do with air resistance?

Yes, this has to do with air resistance. When you skydive, you velocity doesn't increase indefinitely because the upward force of air resistance eventually balances the downward force of gravity. At that point, you reach a constant velocity (called "terminal velocity"). Just how large this terminal velocity is depends on your shape. It is possible to increase your terminal velocity by rolling yourself into a very compact form. In that case, you can overtake a person below you who is in a less compact form. In the case of James Bond chasing a plane, the plane was in a steep dive with its propeller helping to push it downward. The plane would have an extremely high terminal velocity that Bond could never hope to match. He couldn't possible overtake a diving plane.

Can you clarify the support forces becoming strong enough to keep the cart from entering the ramp?

As the cart rolls on the ramp, the forces between the cart and ramp naturally adjust themselves until the ramp pushes out on the cart just enough to keep it from accelerating toward or away from the ramp's surface. If the ramp pushed too hard, the cart would accelerate away from the ramp and soon lose contact with it. If the ramp pushed too little, the cart would accelerate toward the ramp and soon burrow into it.

What is moment of inertia?

It's the measure of an object's rotational inertia-it's resistance to angular accelerations.

If you're sitting in a chair, you're experiencing two forces: the force of gravity and the force of the chair. The net force is zero. If mass is the measure of inertia on a body experiencing no outside forces and an object not experiencing outside forces moves at constant velocity, does that mean that the body in the chair doesn't have a constant velocity or a velocity at all? We still have mass.

No, an object's mass doesn't depend on whether or not it's moving. Mass is the measure of an object's inertia, its resistance to acceleration. Inertia is an object's tendency to move at constant velocity. When you're sitting in a chair, your mass is what it normally is. If you were sitting in a catapult it will still be what it normal is, even after they cut the cord and you begin to accelerate upward.

You did an experiment with work using a 15 N cart and a 0.2 m distance. Then work equals force times distance equals 3.0 J. Does this mean that the force equals the weight of the object?

Yes, in this case it is. When you lift an object upward at constant velocity, the upward force you exert on it must be equal to its downward weight. That way, the net force on it will be zero and it won't accelerate. To get the cart moving upward you must briefly pull upward on it with a slightly larger force and to stop the cart moving upward you must briefly pull upward on it with a slightly smaller force. But during the main part of the lifting, you just have to balance its weight.

Is rotational inertia the same as moment of inertia?

Rotational inertia is a concept: the tendency of an object to continue spinning or not spinning. Moment of inertia is a quantitative measure of an object's rotational inertia: how much torque does it take to cause a certain angular acceleration to occur.