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

In summary, the solution used polar coordinates and when calculating the acceleration of the collar with respect to the rod, only the radial component of acceleration was considered. This is because the collar is on the rod, resulting in the transverse acceleration component being the same for both. Therefore, the transverse component of acceleration for the collar with respect to the rod is 0. Additionally, the rod will apply torque as needed to force the collar.
  • #1
mingyz0403
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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?
 

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  • #2
mingyz0403 said:
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.
 
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  • #3
BvU said:
Correct. The rod forces the collar with whatever torque is necessary.
Ok, Thank you.
 

1. What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In other words, the greater the force applied to an object, the greater its acceleration will be, and the more massive an object is, the less it will accelerate under the same force.

2. How does the Second Law apply to a collar sliding on a rotating rod?

In this scenario, the collar experiences two forces: the force of gravity pulling it downward and the force of the rod pushing it in a circular motion. According to Newton's Second Law, the net force on the collar will determine its acceleration. If the force of gravity is greater, the collar will slide down the rod at a faster rate. If the force of the rod is greater, the collar will move in a circular motion at a faster rate.

3. How does mass affect the acceleration of the collar?

The mass of the collar will directly affect its acceleration according to Newton's Second Law. The greater the mass of the collar, the more force will be needed to accelerate it at the same rate as a lighter collar. This means that a heavier collar will move slower on the rotating rod compared to a lighter collar under the same force.

4. What happens to the acceleration of the collar if the force of the rod is increased?

If the force of the rod pushing the collar in a circular motion is increased, the acceleration of the collar will also increase. This is because the net force acting on the collar is greater, causing it to accelerate at a faster rate. However, the acceleration will still be affected by the mass of the collar, so a heavier collar will still move slower than a lighter one under the same force.

5. How does the direction of the net force affect the motion of the collar?

The direction of the net force will determine the direction of the acceleration of the collar. If the net force is in the same direction as the motion of the collar, it will increase its speed. If the net force is in the opposite direction, it will decrease the speed of the collar. If the net force is perpendicular to the motion of the collar, it will cause the collar to change direction but not necessarily change its speed.

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