Linear acceleration is the acceleration of an object with the gravitational component mathematically removed. It represents only the acceleration due to actual motion.
Discover FizziQ
How to measure it in class
Steps:
- Select linear acceleration in FizziQ
- Note that when stationary, the reading is approximately 0
- Move the phone and observe acceleration spikes
- Compare with absolute acceleration readings
Learn more
Linear acceleration is calculated by subtracting the gravity vector from absolute acceleration. It’s useful for:
- Step counting (pedometers)
- Gesture recognition
- Motion gaming
Scientific activities on this topic
Several experiments easily performed with a smartphone, tablet, or computer allow you to measure and study linear acceleration.
- 1: What is an accelerometer - Discover the concept of linear acceleration: https://www.fizziq.org/en/activities/what-is-an-accelerometer/
- 2: Takeoff - Calculating the takeoff speed of an airliner: https://www.fizziq.org/en/activities/takeoff/
- 3: A kilometer on foot - Using the accelerometer to build a pedometer: https://www.fizziq.org/en/activities/one-kilometer-walk/
- 4: SpaceX rocket - Kinematic analysis of a rocket’s velocity: https://www.fizziq.org/en/activities/space-x-rocket/
Formula
Linear acceleration is derived from absolute acceleration by subtracting g:
a_linear = a_absolute - g
Meaning:
- a_linear: acceleration due to motion alone (m/s2)
- a_absolute: total acceleration measured by the sensor (m/s2)
- g: gravitational acceleration vector (9.81 m/s2 downward)
At rest: a_linear = 0 m/s2 In free fall: a_linear = -g (approximately) -9.81 m/s2
Examples
-
The smartphone in a runner’s pocket measures the accelerations of each stride
-
A driving application detects sudden braking through linear acceleration
-
The smartphone’s pedometer counts steps by detecting linear acceleration spikes
-
Automotive crash tests measure the linear acceleration experienced by test dummies
-
The fall detection system of a smartwatch uses linear acceleration
FAQ
Q: Why is linear acceleration zero at rest? A: By design, linear acceleration is obtained by subtracting g from the raw measurement. At rest, the raw measurement equals g, so the subtraction gives zero.
Q: Is linear acceleration more accurate than absolute acceleration? A: It is less accurate because it depends on a sensor fusion algorithm to estimate g. Errors in this estimation create a residual offset, visible when the smartphone is tilted quickly.
Q: Can you calculate velocity from linear acceleration? A: In theory yes, by integration. In practice, errors accumulate rapidly and the calculated velocity drifts after a few seconds. This method is only reliable for short movements.
Q: What is the difference between linear acceleration and tangential acceleration? A: FizziQ’s linear acceleration measures total acceleration without g in all three directions. Tangential acceleration in physics specifically refers to the component parallel to the trajectory.
Q: Why does the smartphone use multiple sensors to calculate linear acceleration? A: The gyroscope measures the smartphone’s rotation, which allows knowing its orientation relative to vertical. This orientation is necessary to determine the direction of g and correctly subtract it from the accelerometer measurement.
Related concepts
Absolute acceleration - Accelerometer - Gravitational acceleration - Velocity - Rectilinear motion - Sensor fusion - Gyroscope