Force applied at centre of mass

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SUMMARY

When a force is applied at the center of mass of an object, the object will only translate without any rotation. This is mathematically proven by the definition of torque, which is the cross product of the position vector (r) from the center of mass to the point of force application and the force vector. If the position vector (r) is zero or parallel to the force vector, the torque is zero, resulting in no rotational motion.

PREREQUISITES
  • Understanding of basic physics concepts, specifically Newton's laws of motion.
  • Familiarity with vector mathematics, including cross products.
  • Knowledge of torque and its relation to rotational dynamics.
  • Concept of center of mass in rigid body mechanics.
NEXT STEPS
  • Study the mathematical derivation of torque in rigid body dynamics.
  • Explore the implications of applying forces at different points relative to the center of mass.
  • Learn about the principles of rotational motion and angular momentum.
  • Investigate real-world applications of center of mass in engineering and physics.
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Physics students, mechanical engineers, and anyone interested in understanding the principles of motion and forces in rigid bodies.

chandran
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If a force is applied at centre of mass the object will only translate and not rotate. Can anyone proove this mathematically?
 
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Torque is the cross product of the vector from the center of mass to the point where the force is applied (r), and the force. If r is zero, or r is parallel to the force, there will be no torque, and so no rotational force.
 

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