# Acceleration, velocity and position

I was given a bunch of data points (time vs angular acceleration). So I did some curve fitting and came up with an equation for angular acceleration. My problem is: If I'm given an equation for angular acceleration as a function of time and I want to find an equation for angular displacement as a function of time, how many initial conditions will I need to know to do this?

If I assume that initially the system is at rest with angular displacement=0, is that enough?? Is angular velocity=0 as well then?I'm thinking its not because from the data points I have angular acceleration at t=0 is a non-zero number.

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It is enough information, because when given a equation of acceleration, and needing to find position, you must integrate twice (once to go from acceleration to velocity, the other to go from velocity to position). So when you integrate the first time, you will get a constant, that is your initial velocity. The second time you integrate the constant will be your initial position. So in short, yes all you need to know are those two.

Yes when you see "initially at rest" the automatically means the initial velocity is 0.

Also, if your initial velocity is 0, that does not necissarily make your initial acceleration 0.

Thanks...so the 2 constants of integration after doing the integration and subbing in omega=0 and theta=0 at time=0 are zero then Could you explain though how if the system is at rest initially, how there can be an initial angular acceleration?

daniel_i_l
Gold Member
Lets say that the system was spinning to the left. If we know apply a constant force to the right, then it will slow down, get to zero, and start speeding up in the right direction. But in the middle it had 0 speed even though it had acceleration.