Is Vertical Acceleration Always Zero?

No. Vertical acceleration is zero only when the net vertical force on an object is zero in the chosen frame of reference; otherwise it is not. For example, a projectile near Earth accelerates downward at about 9.81 m/s², while an object resting on a table or falling at terminal velocity has zero vertical acceleration because forces balance.

What Determines Vertical Acceleration?

Vertical acceleration, usually denoted a_y, follows Newton’s second law: a_y = ΣF_y / m. It depends on the sum of all vertical forces—gravity, normal force, lift, thrust, drag, buoyancy, and tension—along with the reference frame. With upward defined as positive, if the upward and downward forces cancel, a_y = 0; if they do not, a_y ≠ 0. Near Earth’s surface and ignoring air resistance, many motions have a_y ≈ −g ≈ −9.81 m/s² (downward). In real conditions, drag, thrust, and contact forces can make a_y smaller, larger, or zero.

When Vertical Acceleration Is Zero

The following common situations produce zero vertical acceleration because vertical forces balance exactly, resulting in no change in vertical velocity.

• Object at rest on a surface: Normal force equals weight (N = mg), so ΣF_y = 0 and a_y = 0.
• Constant-speed elevator: Once moving steadily (no speeding up or slowing down), tension/drive force and weight balance, so a_y = 0.
• Terminal velocity in air or fluid: Drag equals weight (D = mg), giving zero net vertical force and thus a_y = 0, even though the object keeps moving.
• Level, unaccelerated flight: Aircraft lift equals weight (L = W), so the aircraft has no vertical acceleration (though it may accelerate horizontally).
• Static buoyancy balance: A neutrally buoyant object in water (buoyancy = weight) experiences a_y = 0.

In all these cases, the vertical velocity is either zero or constant because the net vertical force is zero. Any imbalance would immediately create a nonzero vertical acceleration.

When Vertical Acceleration Is Not Zero

These scenarios feature unbalanced vertical forces, which produce a change in vertical velocity according to Newton’s second law.

• Free fall (neglecting drag): a_y ≈ −g downward everywhere near Earth’s surface.
• Projectile motion: Throughout the flight (ignoring drag), a_y remains ≈ −g; horizontal acceleration is approximately zero, vertical acceleration is not.
• Elevators during speed changes: Starting upward or stopping while moving downward gives a_y > 0; starting downward or stopping while moving upward gives a_y < 0.
• Rocket/aircraft climb or descent: If thrust plus lift exceeds weight, a_y > 0 (climb acceleration); if they fall short, a_y < 0 (descent acceleration).
• Mass–spring and oscillations: Vertical acceleration varies with displacement; it’s largest at extreme positions and zero only at the equilibrium crossing.
• Splashdown or impact: During brief contact, large contact forces create large, often upward, vertical accelerations.

Anytime vertical forces do not cancel, the object’s vertical speed will change in time, evidencing nonzero vertical acceleration.

Reference Frames Matter

Measurements of vertical acceleration depend on the frame. In an inertial frame near Earth, a dropped object has a_y ≈ −g. In a non-inertial frame—such as inside a freely falling elevator—apparent weight is zero, and an onboard accelerometer reads 0 g even though gravity is present, because both you and the accelerometer accelerate together. Earth’s rotation also slightly reduces effective gravity at the equator, so g varies by latitude and altitude (approximately 9.78–9.83 m/s² at sea level).

How to Tell If a_y = 0

Use a simple checklist to decide whether vertical acceleration vanishes in a situation.

1. List all vertical forces (weight, normal, lift, thrust component, drag, buoyancy, tension).
2. Choose a sign convention (e.g., up positive) and sum the forces: ΣF_y.
3. If ΣF_y = 0 in an inertial frame, then a_y = 0; otherwise, a_y = ΣF_y / m ≠ 0. In accelerating frames, include inertial/pseudo-forces before summing.

This procedure works for everyday problems and clarifies when “zero vertical acceleration” actually applies.

Common Misconceptions

These misunderstandings often lead to incorrect conclusions about vertical acceleration.

• “If speed is constant, acceleration is zero.” Not necessarily; acceleration concerns changes in velocity, including direction and vertical component. An object can move at constant speed but still have nonzero vertical acceleration if forces don’t balance vertically.
• “In orbit there’s no gravity.” Gravity is present and provides the centripetal acceleration. Astronauts feel weightless because they’re in continuous free fall, not because g = 0.
• “At the top of a projectile’s arc, acceleration is zero.” Velocity’s vertical component is momentarily zero there, but acceleration remains ≈ −g.

Keeping these points in mind prevents mixing up zero velocity with zero acceleration and distinguishes forces from sensations like weightlessness.

Key Equations and Typical Values

Core relation: a_y = ΣF_y / m, with upward positive by convention. Near Earth’s surface, g ≈ 9.81 m/s² downward; at sea level it varies roughly 9.78–9.83 m/s² depending on latitude. Drag often scales with speed (linearly at low speeds, quadratically at higher speeds), so a_y in real falls tends toward zero as terminal velocity is reached. An ideal accelerometer at rest on the ground reads +1 g upward (support force), while in free fall it reads 0 g.

Summary

Vertical acceleration is not always zero. It is zero only when vertical forces balance in the chosen frame—such as on a stable surface, at terminal velocity, or during steady-level flight. In free fall, projectile motion, and any situation with unbalanced vertical forces, vertical acceleration is nonzero, typically near −9.81 m/s² close to Earth. The key is to sum vertical forces in the appropriate frame: if ΣF_y = 0, then a_y = 0; if not, it isn’t.