If you have the initial and final angular velocities (ω₁ and ω₂) and the time it takes (t) without the radius given, you can calculate the angular acceleration (α) using the formula:
α = (ω₂ - ω₁) / t
To find the linear acceleration (a), you need the radius (r) or the distance from the axis of rotation. The linear acceleration is related to the angular acceleration by the equation:
a = α * r
where r is the radius or the distance from the axis of rotation to the point of interest. The linear acceleration is the tangential acceleration experienced by a point rotating at a given radius.
Therefore, if you have the radius (r), you can multiply it by the angular acceleration (α) to find the linear acceleration (a) using the formula a = α * r.