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An in-depth exploration of the concepts of torque and equilibrium, including definitions, formulas, calculations, and problem-solving techniques. Learn about Archimedes' Lever Rule, the General Lever Rule, and how to calculate torque using different methods. Discover the conditions for equilibrium and how to solve static equilibrium problems.
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Lecture 8 Pre-reading: KJF §8.1 and 8. 1
At equilibrium (and with forces 90° to lever): r 1 F 1 = r 2 F 2 2 2 3
For general angles r 1 F 1 sin! 1 = r 2 F 2 sin! 2 We call rF sin! = "# torque S.I. unit of torque : newton metre (Nm) At equilibrium, the magnitude of torques exerted at each end of lever are equal KJF §7. 3 Crudely speaking, torque is "twisting or turning ability" of a force that can:
4 4 Note:
Choose a sign convention (e.g. anti-clockwise +ve), then decide in which direction force is pulling or pushing lever. Write that sign in front of your answer. Method 1: If you're given r and !, use formula for torque (magnitude)
Example : Calculate torque on lever exerted by hand:
7 Calculating torque (2) Method 2:
from axis to the “line of action”, then use formula
(i.e. d $=$0) then " = 0 7 8 Opening a door
12 Adding up Torques: Example
#! net torque = '" = " 1 + " 2 = 2.45 + (–2.50) = –0.05 Nm (i.e. clockwise)
19
Too much cargo is loaded at the back. If the wheel is chosen as the rotation axis, all resulting torques are acting in the clockwise direction. There is no torque opposing the torque due to the weight of the system, hence there is a net clockwise torque. The system will rotate until the cart hits the ground. The donkey will be lifted off the ground. 19 20 20 21 21 22
Neutral: with a small displacement, remains at new position. Stable: with a small displacement, returns to original position. Unstable: with a small displacement, continues to move away from equilibrium position. KJF §8. 22 23
net torque around X X 24 W
NO net torque around X X
25 W
net torque around X X
25 26 26
Momentum, impulse and energy Read: KJF §9.1, 9.