## I am a huge figure skating fan and was wondering if you could explain to me the …

#### I am a huge figure skating fan and was wondering if you could explain to me the physics of a triple axle jump? My friends and I are always asking ourselves how it’s done. — AF

While I don’t know the details of the jump, there are some basic physics issues that must be present. At a fundamental level, the skater approaches the jump in a non-spinning state, leaps into the air while acquiring a spin, spins three times in the air, lands on the ice while giving up the spin, and then leaves the jump in a non-spinning state. Most of the physics is in spin, so that’s what I’ll discuss.

To start herself spinning, something must exert a twist on the skater and that something is the ice. She uses her skates to twist the ice in one direction and, as a result, the ice twists her in the opposite direction. This effect is an example of the action/reaction principle known as Newton’s third law of motion. Because of the ice’s twist on her, she acquires angular momentum during her takeoff. Angular momentum is a form of momentum that’s associated with rotation and, like normal momentum, angular momentum is important for one special reason: it’s a conserved physical quantity, meaning that it cannot be created or destroyed; it can only be transferred between objects. The ice transfers angular momentum to the skater during her takeoff and she retains that angular momentum throughout her flight. She only gives up the angular momentum when she lands and the ice can twist her again.

During her flight, her angular momentum causes her to spin but the rate at which she spins depends on her shape. The narrower she is, the faster she spins. This effect is familiar to anyone who has watched a skater spin on the tip of one skate. If she starts spinning with her arms spread widely and then pulls them in so that she becomes very narrow, her rate of rotation increases dramatically. That’s because while she is on the tip of one skate, the ice can’t twist her and she spins with a fixed amount of angular momentum. By changing her shape to become as narrow as possible, she allows this angular momentum to make her spin very quickly. And this same rapid rotation occurs in the triple axle jump. The jumper starts the jump with arms and legs widely spread and then pulls into a narrow shape so that she spins rapidly in the air.

Finally, in landing the skater must stop herself from spinning and she does this by twisting the ice in reverse. The ice again reacts by twisting her in reverse, slowing her spin and removing her angular momentum. She skates away smoothly without much spin.

## How do slot machines work?

#### How do slot machines work? — DD, Thunder Bay, Ontario, Canada

A slot machine is a classic demonstration of rotational inertia. When you pull on the lever, you are exerting a torque (a twist) on the three disks contained inside the machine. These disks undergo angular acceleration—they begin turning toward you faster and faster as you complete the pull. When you stop pulling on the lever, the lever decouples itself from the disks and they continue to spin because of their rotational inertia alone—they are coasting. However, their bearings aren’t very good and they experience frictional torques that gradually slow them down. They eventually stop turning altogether and then an electromechanical system determines whether you have won. Each disk is actually part of a complicated rotary switch and the positions of the three disks determine whether current can flow to various places on an electromechanical counter. That counter controls the release of coins—coins that are dropped one by one into a tray if you win. Sadly, computerized gambling machines are slowly replacing the beautifully engineered electromechanical ones. These new machines are just video games that handle money—they have little of the elegant mechanical and electromechanical physics that makes the real slot machines so interesting.

## When a rear-wheel drive truck goes up a hill, do its rear wheels gain traction b…

#### When a rear-wheel drive truck goes up a hill, do its rear wheels gain traction because of a transfer of weight to its rear wheels? I think it depends on the center of gravity, right? — DA, Issaquah, Washington

The traction a wheel experience depends largely on how hard it’s being pushed into the roadway. When the truck is on level pavement, the roadway prevents the wheel from sinking into it by pushing upward on the wheel with a force called a support force. Because a wheel’s traction is roughly proportional to the support force it’s experiencing, the harder the wheel is pushed into the roadway, the more traction that wheel has.

Since a truck has its heavy engine in front, the front wheels bear more of its weight than the rear wheels and they experience more traction than the rear wheels. But as the truck tilts upward on the hill, the weight of its engine is born more and more by the rear wheels. In physics terms, the truck’s center of gravity, which is almost over the front wheels while the truck is level, shifts to be more and more over the rear wheels as the truck tilts upward.

However, the extra weight that the rear wheels are supporting as the truck tilts doesn’t improve their traction. That’s because this extra weight isn’t being supported entirely by support forces—much of it is being supported instead by friction between the rear wheels and the roadway. In fact, the support forces exerted by the roadway on the rear wheels to keep them from sinking into the pavement actually become weaker as the truck tilts uphill, so the truck loses traction as the tilt increases. Since traction is responsible for the friction that is also supporting the truck, the truck is in danger of slipping down the road. There is clearly a limit to how steep the roadway can get before the truck begins to slide.

## Why are sparks generated when iron is brought in contact with a spinning grindin…

#### Why are sparks generated when iron is brought in contact with a spinning grinding wheel? — JF, Rochester, NY

When the iron touches the spinning wheel, the two experience sliding or “dynamic” friction—the iron acts to slow the wheel while the wheel acts to move the iron. Because you hold the iron in place, it doesn’t move but its surface begins to experience severe wear—the iron is skidding across the surface of the wheel. Sharp projections from the wheel are tearing particles away from the iron and throwing them in the direction of the wheel surface’s motion. Because the two surfaces, iron and wheel, are pushing on one another and they are moving relative to one another in the directions of their forces, they are doing physical work on one another—meaning that they are exchanging energy. This energy is actually being converted from the wheel’s rotational energy into thermal energy in the iron and in the wheel, both of which become hot. You can feel similar heating by rubbing you hands against one another vigorously. The wheel’s surface begins to glow red-hot and the particles that fly off the iron emerge so hot that they burn in the air. The sparks you see are the iron particles burning up. Depending on what type of iron or steel you use, you’ll see different spark patterns. An expert can actually identify an alloy by this pattern.

## I have read that sometimes two very slick things rubbing together have more fric…

#### I have read that sometimes two very slick things rubbing together have more friction than two rough things. Is that true? Why? — A

Friction is caused by contact and collisions between the tiny projections that exist on all surfaces. When you put one block on top of another, the tiny projections on the bottom of the upper block touch the tiny projections on the top of the lower block. If you then try to slide one block across the other, these projections begin to collide with one another and they oppose the sliding motion.

If the two blocks have rough surfaces, then the projections that are colliding are obvious to your eyes. But if the two blocks have very smooth surfaces, you can’t see their surface projections. However, the invisibility of these projections doesn’t make them insignificant. Even the smoothest surfaces are rough at the atomic scale. When you press two smooth surfaces against one another, their microscopic projections still touch one another and those projections still collide when you try to slide the surfaces across one another. In short, smooth surfaces still experience friction.

But it’s also possible for attachments to form between portions of the two smooth surfaces when they touch. This molecular adhesion makes it even harder to slide the two surfaces across one another. You can feel this adhesion when you press two pieces of very clean glass against one another—they form bonds that partially stick them together. Actually, this sort of sticking would be quite common if it weren’t for water. Almost all surfaces are coated with a layer or two of water molecules. These water molecules lubricate the interface between any two surfaces and make it hard for those surfaces to stick to one another. But if you get rid of the water molecules, the sticking becomes quite severe. This effect causes trouble in my laboratory, where sliding mechanisms that move easily in air stop working properly when we put them in a vacuum chamber and remove the water on their surfaces.

## If energy is always conserved, why does a pendulum eventually stop swinging if y…

#### If energy is always conserved, why does a pendulum eventually stop swinging if you leave it alone?

The pendulum experiences friction and air resistance, both of which extract energy from the pendulum. Friction turns that energy into thermal energy and air resistance transfers the energy to the air.

## If there were no friction or air resistance, would the bowling ball pendulum con…

#### If there were no friction or air resistance, would the bowling ball pendulum continue in motion forever?

Yes. If the pendulum had no way to convert its energy into thermal energy (e.g., via friction) and no way to transfer that energy elsewhere (e.g., via air resistance), it would continue to swing forever. While its energy would transform from gravitational potential energy (at the ends of each swing) to kinetic energy (at the middle of each swing) and back again, over and over, the total amount of energy it has won’t change.

## In class, you sat motionless on a cart with a ball in your lap. You said that yo…

#### In class, you sat motionless on a cart with a ball in your lap. You said that your momentum was zero. You then threw the ball in one direction and you began moving in the other direction. You said that your momentum was still zero. How can your momentum be zero if you are moving?

In both cases, I was referring to the total momentum of the ball and me. The total momentum of the ball and me was zero before I threw the ball and it was still zero after I threw the ball. However, before I threw the ball nothing was moving and after I threw the ball the two of us were moving in opposite directions. It was our total momentum that was zero after the throw, not our individual momenta. While the ball and I each had a nonzero momentum after the throw, our momenta were equal in amount but opposite in direction—the ball’s momentum was exactly opposite mine. If you were to add our momenta together, they would sum to zero. Since momentum is conserved and we couldn’t exchange momentum with anything around us, the ball and I began and ended with the same total amount of momentum: zero.

## Piling sandbags in the back of a truck would increase friction between the wheel…

#### Piling sandbags in the back of a truck would increase friction between the wheels and the ground, but wouldn’t it also increase the truck’s inertia, making it harder to stop on an icy road?

Adding sandbags to the back of a pickup truck increases the truck’s traction and adds to the truck’s mass. Fortunately, the truck’s traction increases more dramatically than its mass and it becomes easier to start and stop the truck, rather than the reverse. That’s because even a modest amount of sand can double the force pressing the rear wheels against the road and thus double the frictional forces the wheels can experience. That same amount of sand won’t double the total mass of the truck.

## When friction is made by two atoms rubbing

#### When friction is made by two atoms rubbing — it makes heat. But how and why? — GN, Marine City, MI

When two surfaces slide across one another, some of the mechanical energy in those surfaces is converted to thermal energy (or heat). That’s because the surfaces are microscopically rough and their atoms collide as the surfaces slide pass one another. Each time a collision occurs, the atoms that collide begin to vibrate more vigorously than before. In this process, the surfaces lose some of their overall mechanical energy but the atoms gain some randomly distributed local vibrational energy—more thermal energy. Those surface atoms become hotter. As the sliding continues, large regions of the surfaces become hotter and the surfaces lose much of their energy. If you don’t push them to keep them sliding across one another, they’ll come to a stop as all their mechanical energy is converted into thermal energy.