1. the quantities of motion-position, velocity, acceleration, mass, and force,
2. the differences between speed, velocity, and acceleration,
3. what weight is and how it differs from mass,
4. about work and energy,
5. about rotational motion,
6. and about friction.

For now, all you need to know about the Segway HT is that you stand on a platform between two forward-facing wheels, one to the left of your feet and one to the right. When you lean forward, the two wheels spin forward and the platform drives forward. When you lean backward, the two wheels spin backward and the platform drives backward. And when you turn a steering control, the two wheels spin at different rates or in different directions and the platform pivots so that you face a new direction. For more on the Segway HT, you can watch videos of it in action at http://www.segway.com/video/ or visit the Segway web site at www.segway.com.

1. You step onto the platform of the HT and stand there motionless. While you remain still, (A) what forces (if any) are acting on you and (B) what is the net force on you?

Answer: (A) You experience your weight downward and an upward support force from the HT on your feet. (B) The net force on you is zero.

Why: You are not accelerating, so the net force you are experiencing must be zero. However, gravity hasn't vanished so you must be experiencing your downward weight. To balance that weight and bring the net force on you to zero, the platform must be exerting an upward support force on you equal in amount to your weight.

2. You lean forward and the HT begins to pick up speed in the forward direction. During this period time, (A) are you accelerating and, if so, in which direction and (B) do you have a velocity and, if so, in which direction?

Answer: (A) You are accelerating forward and (B) your velocity is forward. (Note: for the first instant of this time period, your velocity is actually zero.)

Why: Since you are heading forward, your velocity must be forward. That forward velocity is increasing, so you must be accelerating in the forward direction.

3. The HT reaches full speed and you begin to ride it up a smooth, uniform ramp. As you ride straight ahead up this ramp at full speed, what are (A) your acceleration, (B) your velocity, (C) the net force you are experiencing, and (D) the force your feet are exerting on the platform of the HT?

Answer: (A) Your acceleration is zero, (B) your velocity is 12.5 mph directly up the ramp, (C) the net force on you is zero, and (D) your feet are exerting a downward force equal to your weight on the platform of the HT.

Why: You are coasting at a constant velocity, which is clearly directed up the ramp and equal in amount (or magnitude) to the maximum speed of the HT, or 12.5 mph. Since your velocity isn't changing, you are not accelerating and must be experience zero net force. However, you still have weight, so the platform must be exerting an upward support force on your feet with an amount equal to your weight. If the platform pushes up on your feet, then your feet must push equally hard down on the platform. Your feet are thus pushing downward on the platform with a force equal to your weight.

4. The ramp is 3 meters high and its paved surface is 50 meters long. As you and the HT climb this ramp, (A) is one of you (your body and the HT) doing work on the other? (B) If so, which one and how much overall work does that one do on the other?

Answer: (A) Yes. (B) The HT does an amount of work on you equal to the product of 3 meters times your weight.

Why: The HT is pushing upward on your feet and they are moving upward (albeit at an angle). During the travel up the ramp, the HT pushes your feet upward a total of 3 meters and the upward force it exerts on your feet is equal in amount to your weight. The work done by the HT on your feet is equal to force times distance in the direction of that force, or your weight times 3 meters.

5. You return to level pavement and then stop briefly to pick up your extraordinarily heavy backpack. When you start the HT moving forward, you notice that it is now struggling to pick up speed. (A) What aspect of the backpack is affecting the HT's ability to pick up speed and (B) why?

Answer: (A) The backpack's mass is responsible for changing the HT's behavior. (B) Because the backpack increases the mass of the HT's burden, the HT must exert more forward force on you and your backpack to make you accelerate forward at the same rate as before. (Note: an equivalent answer to (B) is that the HT must do more work on you and your backpack to bring you up to cruising speed.)

Why: Since the HT is moving horizontally, its motion is independent of gravity. Support forces conveyed upward from the ground are responsible for supporting your backpack's weight, but making your backpack move horizontally is another matter. With its large mass, your backpack resists acceleration and the HT must push harder on you and your backpack to make the two of you accelerate at the normal rate.

6. You finally reach your friend's home and slow to a stop. As you and the HT are stopping, but are not yet stopped, in which direction are (A) the net force on you, if any, (B) your acceleration, if any, and (C) your velocity, if any?

Answer: (A) The net force on you is backward, (B) your acceleration is backward, but (C) your velocity is forward.

Why: Although your are still moving forward and thus have a forward velocity, your speed is decreasing. You are decelerating or, equivalently, accelerating in the direction opposite your velocity. Your accelerating is backward and the net force that is causing that backward acceleration must itself be backward.

7. As you and the HT come to a stop, but are not yet stopped, what type(s) of force does the pavement exert on the HT and in which direction(s)?

Answer: The pavement exerts an upward support force on the HT and a backward frictional force on the HT. (Note: unless you skid to a stop, that frictional force is static friction.)

Why: Support forces act only are right angles (or perpendicular) to surfaces. Since the pavement is horizontal, its support forces are only vertical. Therefore, the only source for horizontal stopping forces is friction. That friction pushes backward on the wheels of the HT and make it accelerate backward. Since the wheels merely touch and release, and don't ordinarily skid, there is no relative movement of the wheel surface across the pavement. The frictional force is therefore static friction.

8. To impress your friend, you keep the HT in one place but pivot the device rapidly around and around. You begin by (a) pivoting clockwise (as viewed from above) as fast as possible, then (b) reverse directions, and finish by (c) pivoting counterclockwise as fast as possible. During which time or times (a, b, or c) do you (A) have the largest amount of angular velocity, (B) have the largest amount of angular acceleration, (C)experience the largest amount of torque, and (D) have the largest moment of inertia (assume that you remain rigid throughout this stunt)?

Answer: (A) You have the largest amount of angular velocity at times (a) and (c). (B) You have the largest amount of angular acceleration at time (b). You experience the largest amount of torque at time (b). And (D) your moment of inertia is constant throughout this stunt and therefore has the same value at all three times.

Why: The amount (or magnitude) of your angular velocity is greatest when you are spinning fastest. However, the magnitude of your angular acceleration is greatest when your are changing your rate of rotation as rapidly as possible. That rapid angular acceleration, or change in angular velocity, is caused by torque. Thus, at the same time the magnitude of your angular acceleration is at its maximum, so is the magnitude of the torque on you. As a rigid object always spinning around the same axis (vertical), your moment of inertia remains constant.