the conditions that the net force and the net torque both vanish?
for a body to be in equillibrium, exist two condition:
The sum total of forces in the space vectorial must be zero
sum of forces en x equal zero
sum of forces en y equal zero
sum of forces en z equal zero
and the other condition is:
The sum total of torque in the space vectorial must be zero
sum of torque en x equal zero
sum of torque en y equal zero
sum of torque en z equal zero
enjoy the answer
When the net force and the net torque both vanish, it means that the external forces acting on an object do not cause any linear or rotational motion. In other words, the object is in a state of equilibrium. There are two conditions that need to be satisfied for both the net force and net torque to be zero:
1. Net Force (Linear Equilibrium):
The net force is the vector sum of all the external forces acting on an object. For linear equilibrium, the total force acting on the object must be zero. This can be expressed using Newton's first law of motion, which states that an object will remain at rest or continue to move at a constant velocity in a straight line if the net force acting on it is zero. Mathematically, the condition can be written as ΣF = 0, where ΣF represents the vector sum of all the forces.
To determine if the net force vanishes, you need to calculate the vector sum of all the forces acting on the object. If the sum is zero, the object is in linear equilibrium.
2. Net Torque (Rotational Equilibrium):
The net torque is the measure of the rotational force acting on an object. For rotational equilibrium, the total torque acting on the object must be zero. Torque is calculated as the product of the applied force and the lever arm (the perpendicular distance between the axis of rotation and the line of action of the force). Mathematically, the condition for rotational equilibrium can be written as Στ = 0, where Στ represents the sum of all the torques.
To determine if the net torque vanishes, you need to calculate the torque produced by each force acting on the object and then find the vector sum of all the torques. If the sum is zero, the object is in rotational equilibrium.
In summary, for the net force and net torque to vanish, the vector sums of all the forces and all the torques acting on an object must be zero.