Theoretical Mechanics IPSP

2.1 Motivation and outline: forces are vectors
2.2 Sets
2.3 Groups
2.4 Fields
2.5 Vector spaces
2.6. Physics application: balancing forces
2.7 The inner product
2.8 Cartesian coordinates
2.9 Cross products — torques
2.10 Worked example: Calder's mobiles
2.11 Problems
2.12 Further reading

2.12 Further reading

The second chapter of Grossmann (2012)¹⁾ provides a clear and concise introduction to the mathematical framework of vectors with an emphasis on applications to physics problems.

A nice discussion of force and torque balances with many worked exercises can be found in Chapter2 of Morin (2007)²⁾

¹⁾

Siegfried Großmann, 2012, Mathematischer Einführungskurs für die Physik (Springer).

²⁾

David Morin, 2007, Introduction to Classical Mechanics (Cambridge UP).