Question

The angular position of a particle that moves around the circumference of a circle with a radius of 5m has the equation:
theta = a*t^2
Where a is constant.
theta is in radians
t is in seconds
Determine the total acceleration and its intrinsic components for any time t and give the values when t = .5s where a = 3 rad*s^(-2)



I don't understand what it means by intrinsic components or how to find the total acceleration. I tried to use the equations a=v^2/r and v=(2pi*r)/T , but I don't know how I would incorporate time.

Thank you to anyone who can break this down for me

Answer 1

You have two components of acceleration:
a(centripetal) = v^2/r, which is the centripetal acceleration directed inward towards the center of the circle.

dtheta/dt = omega = 2*a*t
v = omega*r

The second component of acceleration is the tangential acceleration, a(tangential) = (d2/dt(theta))*r = 2*a*r, which is directed tangential to the circle.

The magnitude of the acceleration (the total acceleration) is

(a(centripetal)^2 + a(tangential)^2)^0.5