Question

----------------- 50 points ---------------

1. Establish a relationship between linear acceleration and angular acceleration.

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Answer 1

Explanation:

If an object is rotating at angular velocity and angular acceleration , then a point at distance from the axis of rotation will have speed , tangential acceleration , and centripetal acceleration . The linear acceleration of that point is the vector sum of these two perpendicular components of the acceleration.

Answer 2

Answer:

Linear acceleration is the translational acceleration felt by an object. When linear acceleration is applied to a body, the entire body is affected by the acceleration (or the force) at the same time. Angular accleration is the rotational acceleration felt by an object about an axis.

Explanation:

There are two fundamental equation for linear acceleration and angular acceleration; these are:

mx¨=F,θα¨=M.

it holds further M=(x−x0)×F for some center of mass coordinate x0. If you combine these equations you will get a relation between linear and angular acceleration.

In the case of a yoyo you must add some kinematic conditions like

z=Rϕ

with the yoyo radius R, the height coordinate z and the rotation angle ϕ.