B Centrifugal Force in Angular SHM: Explained

[Jon Drake]

Does centrifugal force (mv^2/r) act in any position of angular SHM? Please explain.

 

[PeroK]

Does centrifugal force (mv^2/r) act in any position of angular SHM? Please explain.

You might need to explain your question! Can you give a bit more detail of the scenario you are asking about?

 

[Jon Drake]

Suppose that a bob is suspended by a light string, and the position of the bob is somewhere between its mean and extreme position. Then it does have a velocity and it moves in a circular arc, so (mv^2/r) should act outward. At the same time in angular SHM we take very small angular amplitude, where the object moves almost in a straight path. In that case there is no centrifugal force. So, in a general situation, should we consider the centrifugal force in the free body diagram or not?

 

[PeroK]

Suppose that a bob is suspended by a light string, and the position of the bob is somewhere between its mean and extreme position. Then it does have a velocity and it moves in a circular arc, so (mv^2/r) should act outward. At the same time in angular SHM we take very small angular amplitude, where the object moves almost in a straight path. In that case there is no centrifugal force. So, in a general situation, should we consider the centrifugal force in the free body diagram or not?

There are only two forces: gravity and the tension in the string. The tension cancels out the force of gravity along the line of the string and provides the centripetal force. Gravity acts tangential to the motion.

 

[sophiecentaur]

So, in a general situation, should we consider the centrifugal force in the free body diagram or not?

The force of the string on the bob is centripetal and that is the tension. For a big displacement, the tension will increase noticeably. Remember the g forces on fairground rides? You are 'pulling 3g' at the bottom of a rigid swing that starts off vertical. However, the SHM approximation only applies to small displacements because it is only then that the restoring force is (near enough) proportional to the displacement (which is the definition of SHM).