Download Understanding Torque and Equilibrium: A Detailed Guide and more Schemes and Mind Maps Acting in PDF only on Docsity! Torque and Equilibrium Lecture 8 Pre-reading: KJF §8.1 and 8.2 1 Archimedes’ Lever Rule At equilibrium (and with forces 90° to lever): r1F1 = r2F2 2 2 3 General Lever Rule For general angles r1F1 sin !1 = r2F2 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 §7.2 3 Crudely speaking, torque is "twisting or turning ability" of a force that can: • change the angular velocity of an object (i.e. speed up or slow down rotation) • cause a twisting or bending distortion of an object A force with a "line of action" that does not cross the axis of rotation results in torque. What is torque? 4 4 Note: • torque is measured about a particular point. Usually this will be a hinge, pivot or axis • torque has a sign. All forces that tend to rotate the object in the same direction produce torque with the same sign 5 5 6 Calculating torque (1) 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) # " = r$F sin! # (Note: sin! = sin%, ! it doesn’t matter which angle you use) Example: Calculate torque on lever exerted by hand: 6 7 Calculating torque (2) Method 2: # If you're given d the “perpendicular distance” from axis to the “line of action”, then use formula # " = d F # If the “line of action” crosses the axis (i.e. d$=$0) then " = 0 7 8 Opening a door • If r is perpendicular to F, then torque " = r F • If r is not perpendicular to F, then torque " = r F sin! where ! is the angle between r and F Axis of rotation r F • What happens if you push in the middle of the door; do you need more or less force? Why? • What happens if you push along a line passing through axis of rotation? Explain. 8 9 Problem The length of a bicycle pedal arm is r$=$0.152$m, and a downward force of F$=$111$N is applied by the foot. What is the magnitude of torque about the pivot point when the angle ! between the arm & vertical is; (a) 30.0°? (b)# 90.0°? (c) 180.0°? [8.44 Nm, 16.9 Nm, 0.00 Nm] 9 10 Adding up Torques We will only consider torques acting in 2D (flat on page) • Choose a sign convention (e.g. anti-clockwise is positive). • Choose the rotation axis around which to calculate torque (unless it's already given). • Draw the line of action for each force • For each force, calculate the resulting torque (including sign). • Add up all the torques. KJF §7.2, see p. 214 10 11 F1 F2 11 12 Adding up Torques: Example # torque 1; "1 = –rF1 sin! = –0.5 & 10 & sin 30 = –2.50 Nm # torque 2; "2 = +mgd = 1 & 9.8 & 0.25 = +2.45 Nm # ! net torque = '" = "1 + "2 = 2.45 + (–2.50) = –0.05 Nm (i.e. clockwise) 12
