Engineering Newton’s Second Law of Motion — Collar sliding on a rotating rod

[mingyz0403]

Homework Statement

The horizontal rod OA rotates about a vertical shaft according to the relation dθ/dt=10t, where
dθ/dt and t are expressed in rad/s and seconds, respectively. A 250 g collar B is held by a cord with a breaking strength of 18 N. Neglecting friction, determine,immediately after the cord breaks, (a) the relative acceleration of the collar with respect to the rod, (b) the magnitude of the horizontal force exerted on the collar by the rod.

Relevant Equations

Newton's Second Law

The soultion used polar corrdinates. Acceleration in polar corrdinates have radial and transeverse components.When calculating the acceleration of collar respect to the rod, the solution only calculates the radial component of acceleration. Is it because the collar is on the rod, so the transeverse acceleration component of the collar is the same as the rod. Acceleration of collar respect to rod=Acceleration of collar-Acceleration of Rod. Therefore, the transeverse component of acceleration of collar respect to the rod is 0?

 

[BvU]

Therefore, the transeverse component of acceleration of collar respect to the rod is 0?

Correct. The rod forces the collar with whatever torque is necessary.

 

[mingyz0403]

Correct. The rod forces the collar with whatever torque is necessary.

Ok, Thank you.