# Torque

 Q:     What is torque? A:     Torque is a physical  vector quantity characteristic for an object in rotational motion around a certain given axis.  By definition torque () is the cross product between the vector of position (r) of the point where a force is applied ( from an origin considered to be on the axis of rotation) and the applied force (F)  ( = r x F).   According to the definition of the cross (or vector) product, the magnitude of the torque is equal to the magnitude of r times the magnitude of F multiplied by sine of the angle () between r and F ( = r F sin ).  In this expression for magnitude of the torque, the product (r sin ) is equal to the magnitude of the distance (d) between the axis of rotation and the "line of action" of the force (F) (r sin = d).  This distance (d) is called "arm of the force."  Now, the torque can be expressed as = Fd (torque is equal to force multiplied by the arm of the force.)  Intuitively, torque can be interpreted as "force with a twist" since it results in rotation of the object on which the force is applied. Q:     An electric motor runs at 1000 rpm and delivers 3.0 hp.  How much torque does it deliver? A:     To solve this problem we need to convert to SI units. P =        so        =  P/ Angular velocity () = 1000 rpm = 1000 rev/min * 1 min/60 sec                                = 16.67 rev/sec * 2 rad/rev =  104.72 rad/sec Power (P) = 3.0 hp = 3.0 hp * 745.70 Watt/hp = 2237.1 Watt =  P/ =  (2237.1 Watt) / (104.71 rad/sec) = (2237.1 N m/sec) / (104.71 rad/sec)  = 21.36 N m

## References

### Equations

Rolling Bodies
 v cm = R
Torque as a Vector
 = rF sin = r F = r F

# Mechanics List of Topics

 Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of Rigid Bodies Elasticity Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical Oscillations Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy and Work Circular Motion of Point-Mass Objects Equilibrium Sound

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