Torque

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Helena Dedic

If you need to understand the concept of center of mass, please see the link below:
CENTER OF MASS

  • A force causes a free object to move in a translational motion if it is applied at the centre of mass of the object or the line of force passes through the centre of mass.

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  • When a force is not applied at the centre of mass of a free object or when the line of force does not pass through the centre of mass then it causes this object to move in a complex way that involves both translation (i.e.: movement of the center of mass) as well as rotation (i.e.: movement around the center of mass.)

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  • OBSERVATIONS OF AN OBJECT:
a) When a force acts at the pivot or when a line of force passes through the pivot, 
the object does not begin to rotate.

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b) When a force acts at some distance from the pivot, the object begins to rotate.

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  • Lever arm is a vector that points from the pivot to the point where the force acts.

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  • TORQUE: A cause of a change of the angular velocity (e.g.: a rotating wheel stops or it begins to rotate faster.
The symbol for torque is .
  • Magnitude and direction of the torque: The magnitude of the torque depends on the magnitude of the lever arm, the magnitude of the force and the angle between these two vectors:

In special cases where the axis of rotation is given: The torque is positive when the torque causes the object to rotate in the counter-clockwise direction and negative when the torque causes the object to rotate in the clockwise direction.

  • In general the torque is a vector product of the lever arm and the force:



EXERCISES ON TORQUE

Static Equilibrium Revisited

  • An object is in static equilibrium if and only if and , where the net torque is the sum of all torques and the net force is the sum of all forces acting on an object.

  • Static equilibrium problem solving strategy:

  1. Determine all forces acting on an object and draw an arrow for each force indicating:
    • A point where this force is applied
    • In which direction this force acts
  2. For each force:
    • Identify the magnitude and the direction of lever arm
    • Draw a diagram consisting of lever arm and force vectors and determine the angle between these two vectors
    • Determine the direction of the torque and then compute its magnitude.
  3. Substitute into the equation
  4. Select the coordinate system
  5. Draw a free-body diagram
  6. Compute the components of the forces
  7. Substitute into the equations and
  8. Solve the system of three equations using the method of substitution



EXERCISES ON STATIC EQUILIBRIUM