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Velocity Vector and Accelerometer

The velocities in a two-dimensional motion can point along with the diagonal directions therefore it is more complex than a one-dimensional motion. Let us consider the example of a cricket ball moving diagonally with a velocity v. The velocity of motion of the cricket ball is divided into horizontal component vx and vertical component vy to simple calculations.

The calculation of both horizontal and vertical directions of the cricket ball in one single equation becomes difficult. The division of the velocity vector into two components turn one difficult problem into two easier problems. The breaking of vectors into components will work for vectors like forces, momentum, electric field also.

How to break a vector into components?

The diagonal vector is divided into two perpendicular components. Therefore the velocity and its components are v, vx and vy. Trigonometric rules can be applied to the velocity vector component and its magnitude. In the triangle below vx is treated as the adjacent side, vy is the opposite side. Therefore the vector magnitude and angle can be broken into components.

Velocity Vector and Accelerometer

Sin θ = Vy /v

Cos θ = Vx /v

tan  θ = Vy /Vx

V in these formulas is the magnitude of the total velocity vector which is a positive value. The components Vx and  Vy can be negative if they are pointing in the negative direction.

Determining the angle and magnitude of the vector?

Let us see how vector magnitude and angle can be calculated if the components vx and vy are known. Applying Pythagorean theorem we can find the magnitude of the total velocity vector.

Velocity Vector and Accelerometer

v2 = vx2 + vy2 

By taking the square root, we get the magnitude of the total velocity vector in terms of the component.

If both the components are known the angle of the velocity vector can be calculated using tanθ.

tan θ = Vy/Vx

θ = tan-1( Vy/Vx)

What is an accelerometer?

The tool that is used to measure acceleration is called an accelerometer. Acceleration is the rate of change of velocity of the object. The unit of acceleration is given by metres per second squared (m/s2). The single value of acceleration is cs considered as 9.8 m/s2. This value of acceleration varies with elevation. The acceleration value varies in different planets due to change in gravitational pull.

How does an accelerometer work?

Accelerometers can measure acceleration on one, two or three axes. Smartphones are making use of three-axis module while cars make use of the two axes. Accelerometer contain capacitive plates internally. Some of these capacitive plates are fixed and few are connected to the spring. As the acceleration force acts on the sensor these capacitance moves internally. As these capacitors move internally the capacitance between them changes. The value of acceleration can be calculated from the change in capacitance.

The other form of the accelerometer is the piezoelectric effect accelerometer. They have microscopic crystal structures that get stressed due to accelerative forces.

Connecting to an Accelerometer

Accelerometers will communicate over an analog, digital or pulse-width modulation connection interface.

Analog: These values show acceleration through varying voltage levels. The value of voltage changes from ground to the supply voltage level. The value of acceleration can be found using the ADC on a microcontroller.

Digital: These type of accelerators can communicate over SPI or I2C communication protocol. They are less susceptible to noise when compared to noise compared to analog accelerators.

Pulse- Width Modulation(PWM): Accelerometers that output data over pulse-width modulation (PWM) output square waves with a known period, but a duty cycle that varies with changes in acceleration.

Power of Accelerometer

Accelerometers are low power devices. The voltage required is 5V or less and the current requirement is microampere or milliampere range. The current consumed by an accelerometer depends on the settings.

Application of Accelerometer

  1. Accelerometer protects the hard drive in laptops. If the laptop falls while in use the accelerometer detects the fall and immediately turns off the hard drive to avoid hitting the reading heads into the hard drive platter.
  2. Accelerometer helps to allow the feature of screen rotation in the smartphones/ Accelerometers do this by detecting the orientation of the phone and tells the screen to rotate.
  3. It helps in image stabilization in the camera as accelerometers in the camera can feed secondary correction into the drive so that the sensor or optics compensate for linear or rotational shake.
  4. It detects the vibrations in machines by measuring the dynamic acceleration of a physical object as a voltage
  5. Detects cracks and damages in mechanical components such as pulleys and bearings and therefore are now commonly used corresponding industries.
  6. Accelerometers help detect accidents by analysing the rapid change in acceleration and triggers the deployment of the airbag
  7. It is used in navigation as it provides information on the linear acceleration of the object. Correspondingly, this application of accelerometer in navigation has allowed accelerometers to be used in the navigation of aircraft, spacecraft, missiles, ships and submarines.
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