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S5.6 Torque

[A] Torque

Key Point 5.14

Torque. Applying a force, magnitude F to a point a distance r from point O, results in a torque about O of magnitude
τ=rFsinθ.
The units of torque are N m.
Graphic - No title - torque

There are two equivalent ways of computing the torque:

  • Multiplying the tangential component of the applied force, Ft, by the distance from the rotation axis
    τ=rFt.
Graphic - No title - torque1
  • Multiplying the applied force by r, the perpendicular distance between the rotation axis and an extended line running through the vector F (the line of action of $\vec{F}$).
    τ=rF
Graphic - No title - torque2

[B] The torque vector

Key Point 5.15

Torque vector: The torque about a point O is the vector defined by

\[ \vec{\tau} = \vec{r} \times \vec{F} \]

where $\vec{r}$ is the point at which the force $\vec{F}$ is applied with respect to point O.

Graphic - No title - torquevec

Worked example

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Worked example

A small 0.75kg ball is attached to one end of a 1.25m long massless rod and the other end of the rod is hung from a pivot. When the resulting pendulum is 30 from the vertical, what is the magnitude of the torque from the pivot

Solution

The torque is provided by the component of the ball’s weight acting perpendicular to the rod. At 30 from the vertical this is

Ft=mg sin30

Hence the magnitude of the torque is

τ=rFt=1.25×mg sin30=4.7N m

 
ATurntable Torque

TWhat makes it roll?

Learning Resources

Textbook: HRW Chapter 10.8 and 11.6
Course Questions:
Self-Test Questions: