A uniform disk with radius 0.650 m
and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to θ(t)=(1.10rad/s)t+(6.30rad/s^2)t^2.
Part A
What is the resultant linear acceleration of a point on the rim of the disk at the instant when the disk has turned through 0.100 rev?
Express your answer with the appropriate units.

Explanation:

First, the instant associated to the angular displacement is:

Roots of the second-order polynomial are:

Only the first root is physically reasonable.

The angular velocity is obtained by deriving the angular displacement function:

The angular acceleration is obtained by deriving the previous function:

The resultant linear acceleration on the rim of the disk is:

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