# Calculating the angular acceleration of a swivel seat

• Automotive
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

CWatters
Homework Helper
Gold Member
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
CWatters