Physics - angular acceleration

An object rotates about a fixed axis, and th angular position of a reference line on the object is given by THETA(t)=0.4e^2t, where THETA is in radians, and t is in seconds.

[a.] what is the object's angular acceleration at t = 2 s?

..this is my work so far

THETA(t) = 0.4e^((2)(2))
= 21.8 degrees

21.8 x (Pi/180) = 0.38 rad

should i be using this equation?:

(w2-w1)/(t2-t1) = Angular acceleration


.. and

[b.] What is the tangential AND centripetal acceleration of a point on the object that is 4.0 cm from the axis of rotation?

.. centripetal acceleration's equation would be A = w^2 r
so.. that would be (0.38^2)(4.0) = 0.5776 rad/cm

did i do that right?

and im stuck on how to do the tangential acceleration equation.. can u show me how to work that one out?

thanks for your help!!

You need to take first and second deriviatives of theta(t) to do this problem. Call the angular acceleration "alpha"
theta = 0.4 e^(2t)
omega = d(theta)/dt = 0.8*e^(2t)
alpha = d(omega)/dt = 1.6*e^(2t)

If R is the distance of an object from the axis of rotation,
tangential acceleration = R*(alpha)
centripetal acceleration = R*(omega)^2

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