# Calculating the angular acceleration of a swivel seat

• Automotive
• marellasunny
In summary: The equations of motion for rotation under constant angular acceleration all have equivalents for linear motion under constant acceleration. You could assume it accelerates for 7.5 seconds over 45 degrees, then decelerates for 7.5 seconds over the remaining 45 degrees. Then you can calculate the angular acceleration/deceleration required using the equations of motion.
marellasunny
We have an automotive swivel seat that turns from the initial seating position to the final position outside the vehicle (90 degree swivel in 15 seconds). We would like to calculate the torque required for rotating the seat along with the person. We have calculated the inertia of the movable parts and are left now with the calculation for the angular acceleration variable.
T=I * alpha (assuming friction, gyroscopic effects to be negligible)

I have figured out a few ways. Please verify if I'm in the right path for figuring this out:
1. The whiplash effect from a vehicle crashing into the rear of the vehicle is 40 m/sec2. I could take the angular acceleration of the seat swivelling out as 1/10 th of this i.e. 4 m/sec2, assuming this to be in the comfortable for the passenger...??
2. I do not have a working prototype but I could use a computer chair attached to a lever arm of 400 mm radius such that it swivels 90 degrees. I would then use a dynamometer to measure the torque required directly at the swivelling centre.

Thank you

The equations for linear motion under constant acceleration all have equivalents for rotation under constant angular acceleration. You could assume it accelerates for 7.5 seconds over 45 degrees, then decelerates for 7.5 seconds over the remaining 45 degrees. Then you can calculate the angular acceleration/deceleration required using the equations of motion.

S=ut + 0.5at^2

Where S is the angular displacement in radians (45 degrees = pi/4 radians)
u is the initial angular velocity (0 radians per second).
a is the angular acceleration in radians per second per second
t is time in seconds (7.5)

Rearrange to get a.

The angular acceleration and the moment of inertia can then be used to calculate the torque required.

Angular acceleration of 0.034 rad/sec2 sounds about right for this application. I make the mistake of not considering the right acceleration time- just the 7.5 seconds, in fact the motors would accelerate, steady and decelerate in a trapezoidal fashion. This was very helpful.

CWatters
marellasunny said:
in fact the motors would accelerate, steady and decelerate in a trapezoidal fashion.

In which case you just need to decide the time over which the acceleration phase occurs.

You might also need to allow extra torque for friction, particularly static friction which is usually higher than kinetic friction. Might be necessary to measure it?

## 1. How is angular acceleration calculated for a swivel seat?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. This can be expressed as α = (ω2 - ω1) / t, where α is the angular acceleration, ω2 is the final angular velocity, ω1 is the initial angular velocity, and t is the time interval.

## 3. How does the radius of the swivel seat affect its angular acceleration?

The radius of the swivel seat does not directly affect its angular acceleration. However, the distance from the center of rotation to the point where force is applied can affect the torque and therefore the angular acceleration. A larger radius will result in a greater torque and potentially a higher angular acceleration.

## 4. Can the angular acceleration of a swivel seat be negative?

Yes, the angular acceleration of a swivel seat can be negative if the seat is slowing down or changing direction in a way that decreases its angular velocity. A positive angular acceleration indicates an increase in angular velocity, while a negative angular acceleration indicates a decrease.

## 5. What factors can affect the angular acceleration of a swivel seat?

The angular acceleration of a swivel seat can be affected by various factors, including the applied force, the moment of inertia of the seat, the distance from the center of rotation, and any external forces or friction that may be present. Additionally, the mass and shape of the seat can also impact its angular acceleration.

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