screwdriver.gif (5123 bytes)     Torque     drill.gif (52355 bytes)


Previously Asked Questions

Q:     What is torque?

torque.gif (4497 bytes)A:     Torque is a physical  vector quantity characteristic for an object in rotational motion around a certain given axis.  By definition torque (tau2.gif (826 bytes)) 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)  (tau2.gif (826 bytes) = 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 (phi2.gif (845 bytes)) between r and F (tau2.gif (826 bytes) = r F sin phi2.gif (845 bytes)).  In this expression for magnitude of the torque, the product (r sin phi2.gif (845 bytes)) 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 phi2.gif (845 bytes) = d).  This distance (d) is called "arm of the force."  Now, the torque can be expressed as tau2.gif (826 bytes) = 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 = tau2.gif (826 bytes) omega2.gif (834 bytes)       so        tau2.gif (826 bytes) =  P/omega2.gif (834 bytes)
Angular velocity (omega2.gif (834 bytes)) = 1000 rpm = 1000 rev/min * 1 min/60 sec
                               = 16.67 rev/sec * 2 pi2.gif (831 bytes) rad/rev =  104.72 rad/sec
Power (P) = 3.0 hp = 3.0 hp * 745.70 Watt/hp = 2237.1 Watt

tau2.gif (826 bytes) =  P/omega2.gif (834 bytes) =  (2237.1 Watt) / (104.71 rad/sec) = (2237.1 N m/sec) / (104.71 rad/sec)  = 21.36 N m

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References

Equations

Rolling Bodies
v cm = omega2.gif (834 bytes) R 12-5.gif (284 bytes)
Torque as a Vector
 tau2.gif (826 bytes) = rF sin phi2.gif (845 bytes) = r Fperp.gif (52 bytes) = rperp.gif (52 bytes) F

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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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