Turning effects of forces
Section: Forces, Density and Pressure | Syllabus: Cambridge AS Level Physics 9702
Moments and Turning Effects You saw in Chapter 3 that a force can cause a body to accelerate. Sometimes, however, a force is applied in a way that will make a body rotate, like when a spanner turns a nut.
In cases like these we need to find the force's turning effect, or moment. Figure 4.1: Lever Diagram (Illustrate a lever/spanner. Show Effort force, Load, Pivot/Fulcrum. Mark distance d along the lever and extend the line of action of the force to show the perpendicular distance d cos θ to the pivot.) Moment = Force × Perpendicular Distance Formula: M = F × (d θ) Where: M = Moment (N m) F = Force (N) d = Distance from pivot to force application point.
θ = Angle between the lever and the horizontal (or reference line perpendicular to force). Important The moment is found by multiplying the force by the perpendicular distance from the pivot to the line of action of the force.
If the force is not perpendicular to the lever, you must resolve it (using cos heta) or find the perpendicular distance. Note: The unit is Newton-metre ( extN m), which is not the same as a Joule ( extJ), even though dimensions are similar.
Worked Example: Calculating Moment Question: An effort of 20 N acts vertically downwards at a distance of 75 cm from the pivot. The lever is at an angle of 30° to the horizontal. Calculate the size of the moment caused by the force, and state whether it is clockwise or anticlockwise.
Solution 1. Convert distance to meters: 75 cm = 0.75 m. 2. Calculate perpendicular distance: d_perp = 0.75 30^. 3. Calculate Moment: M = 20 × 0.75 × 30^ = 12.99 N m 13 N m The force produces a clockwise rotation.
Couples and Torque When two forces of equal magnitude act in opposite directions but not along the same line, they form a couple . A couple causes rotation without linear acceleration (resultant force is zero).
Figure 4.3: Couple on a Steering Wheel (Show a steering wheel with radius r. Left hand exerts force F up/right, Right hand exerts force F down/left. Show that total torque = F(2r) = Fd.) Torque of a Couple The product of one of the forces and the perpendicular distance between the forces.
T = F imes d Worked Example: Bicycle Pedals Question: Two feet push on bicycle pedals with a horizontal force of 100 N each. The distance between the pedals is 33 cm. Find the torque. Solution Distance d = 0.33 m.
T = F × d = 100 × 0.33 = 33 N m Centre of Gravity The centre of gravity of an object is the single point from which its weight may be taken to act. For a symmetrical uniform body, this lies on the axis of symmetry.
Figure 4.6: Centre of Gravity of a Ruler (Show a ruler pivoted at one end, but with a single weight arrow W acting downwards from the 50cm mark explicitly labeled 'Centre of Gravity'.) Finding Centre of Gravity (Symmetrical Object) For a square or rectangle, draw diagonal lines from corner to corner.
The point where they cross is the geometric centre and the centre of gravity. Figure 4.8: Square with diagonals.
Interactive revision notes, videos and practice questions load below.