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Explainer Video

Tutor: Labib

Summary

Tilting

​​In a nutshell

Some bodies will be on the point of tilting about a pivot, and using your knowledge of reaction forces you can work out unknowns in a problem.



Tilting 

When a body is on the point of tilting about a pivot, the reaction force at any other support, or tension in a wire, is zero. This allows you to eliminate one unknown, thus making it easier to calcuate any other unknowns.


Example 1

A uniform beam ABABAB with weight of 50N50N50N and a length of 20m20m20m​ rests on supports CCC and DDD. AC=6mAC=6mAC=6m and AD=16mAD= 16mAD=16m. A box is placed down on point AAA and causes the beam to be on the point of tilting about CCC. Find the weight of the box.


Maths; Moments; KS5 Year 13; Tilting


The beam is on the point of tilting, therefore the reaction force at DDD is 0N0N0N. Taking moments about CCC means RCR_CRC​ can be ignored. Take the weight of the box to be xNxNxN. The beam is uniform therefore the centre of mass is at the midpoint of ABABAB.


Equate clockwise and anticlockwise moments:


x×6=50×46x=200x=2006=33.3\begin{aligned}x\times 6&= 50\times 4\\ 6x&=200\\ x&=\dfrac{200}{6} = 33.3\end{aligned}x×66xx​=50×4=200=6200​=33.3​​​


The box has a weight of 33.3N‾\underline{33.3N}33.3N​.


Example 2

A non-uniform rod weighing 30N30N30N with a length of 15m15m15m​ rests on supports AAA and BBB. When a weight of 15N15N15N is added on the end of the rod 3m3m3m to the right of BBB, the rod is on the point of rotating about BBB. Find the distance of the centre of mass of the rod from point BBB.


Maths; Moments; KS5 Year 13; Tilting


Assume the centre of mass gives an anticlockwise moment about point BBB. Taking moments about BBB​, the reaction force at this point can be ignored. The reaction at point AAA is 000. 


Equate clockwise and anticlockwise moments:


30x=15×330x=45x=4530=1.5\begin{aligned}30x&=15\times 3\\30x&=45\\ x&=\dfrac{45}{30} =1.5\end{aligned}30x30xx​=15×3=45=3045​=1.5​​​


Therefore, the distance of the centre of mass of the rod from point BBB is 1.5m‾\underline{1.5m}1.5m​.


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Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Mass, weight and centre of mass

Unit 1

Mass, weight and centre of mass

Centre of mass

Unit 2

Centre of mass

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Tilting

Unit 3

Tilting

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FAQs - Frequently Asked Questions

When a rod is tilting about a point, does the reaction force stay the same?

Taking moments about some other point, the reaction force at the original point can be ignored.

What does a non-uniform rod mean?

A non-uniform rod means the centre of mass does not have to be at the midpoint of the rod.

What is the effect of a tilting rod?

When a body is on the point of tilting about a pivot, the reaction force at any other support, or tension in a wire, is zero.

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