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Up, Down, and Around
Vertical Motion and Circular Paths
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Objects can move in very different paths depending on the forces acting on them. A ball thrown upward moves mainly along a vertical path, a car on a curved road changes direction as it turns, and a satellite follows a nearly circular path around Earth. Studying these motion paths helps students connect force, velocity, acceleration, and energy in real situations.
Upward and downward motion is strongly shaped by gravity, which produces a nearly constant downward acceleration near Earth's surface. Curved and circular motion happen when a force changes the direction of motion, even if speed stays constant. By comparing straight up and down motion with turning and orbiting motion, students can see that the path of an object reveals the forces acting on it.
Key Facts
- Near Earth, vertical acceleration is a = -g = -9.8 m/s^2 if upward is positive.
- For vertical motion, v = v0 + at and y = y0 + v0t + (1/2)at^2.
- At the highest point of an upward throw, v = 0 for an instant but a = -9.8 m/s^2 still.
- Centripetal acceleration for circular motion is ac = v^2/r.
- Centripetal force is Fc = mv^2/r and always points toward the center of the curve.
- If no net force acts, an object continues in a straight line at constant velocity according to Newton's first law.
Vocabulary
- Trajectory
- A trajectory is the path an object follows as it moves through space.
- Acceleration
- Acceleration is the rate at which velocity changes in speed, direction, or both.
- Gravity
- Gravity is the attractive force that pulls objects toward Earth and gives falling objects a downward acceleration.
- Centripetal force
- Centripetal force is the inward net force that keeps an object moving along a curved or circular path.
- Inertia
- Inertia is the tendency of an object to resist changes in its motion.
Common Mistakes to Avoid
- Thinking acceleration is zero at the top of vertical motion, because the velocity is zero there. This is wrong because gravity still acts downward, so acceleration remains -9.8 m/s^2 near Earth.
- Assuming an object in circular motion has no acceleration if its speed is constant. This is wrong because acceleration also includes changes in direction, and circular motion constantly changes direction.
- Drawing centripetal force outward from the circle, because the object seems to be moving away. This is wrong because the actual net force that causes the turn points inward toward the center.
- Using the wrong sign for gravity in vertical equations, because the positive direction was not chosen carefully. This is wrong because inconsistent signs lead to incorrect velocity and position answers.
Practice Questions
- 1 A ball is thrown straight upward at 19.6 m/s from ground level. Ignoring air resistance, how long does it take to reach its highest point and what maximum height does it reach?
- 2 A 2.0 kg object moves in a circle of radius 4.0 m at a speed of 6.0 m/s. Find its centripetal acceleration and the required centripetal force.
- 3 A car moves around a curve at constant speed. Explain why it is still accelerating and identify the direction of the net force.