Rods, hinges and supports
Objective. Model reactions and tensions in supported systems.
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Learn: the key idea
Rods, hinges and supports problems model how a rigid rod is held in equilibrium by a hinge (providing a reaction force at any angle, often resolved into horizontal and vertical components) and additional forces such as a tension in a string or a reaction from a wall or floor. The hinge reaction is typically found using the equilibrium force equations once other forces are known, while the string tension or an angle is often found first using moments about the hinge, which eliminates the unknown hinge reaction from that equation. For example, a rod hinged to a wall and held by a string at an angle requires moments about the hinge to find the tension, then force resolution to find the hinge reaction components.
Worked example
A uniform rod of weight 30 N and length 2 m is hinged at one end and held horizontal by a vertical string at the other end. Find the tension in the string using moments about the hinge.
- 1Weight acts at the midpoint, 1 m from the hinge
- 2Take moments about the hinge: T × 2 = 30 × 1
- 3T × 2 = 30
- 4T = 15 N
Answer: T = 15 N
Concept mastery
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Practice
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Start practisingCommon mistake. Students take moments about a point other than the hinge, leaving two unknowns (hinge force and tension) in one equation. Taking moments about the hinge eliminates the hinge reaction, giving one equation in one unknown.
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