Torque
Torque and Equilibrium Notes
Learning Outcomes
Define moment (torque) and understand it as a 'turning force'.
Calculate moments using the formula t = F imes r.
Apply the principle of moments for equilibrium.
Understand center of mass and stability.
Distinguish between stable, unstable, and neutral equilibrium.
What is a Moment (Torque)?
Definition: A moment or torque is defined as a 'turning force' - the rotational effect of a force about a pivot point.
Factors influencing moment:
(i) The magnitude of the force (F).
(ii) The perpendicular distance from the pivot to the line of action of the force (r).
Formula: t = r F ext{ sin}( heta) Where:
t = moment (N·m)
F = force (N)
r = perpendicular distance from pivot (m)
heta = angle between force and perpendicular distance.
Units of Moment
Units: The unit of moment is Newton-metres (N·m).
Important Note: Newton-metres (N·m) is NOT the same as Joules (J).
Even though 1 Joule = 1 N·m, they represent different physical quantities.
Difference Between Torque and Moments
Torque: Often synonymously used with moment but may refer specifically to rotational effects, especially in angular motion contexts.
Moment: More broadly refers to the concept of 'turning force,' applicable in both linear and rotational contexts.
Pivot and Linear Motion
A pivot is the fixed point around which rotation occurs.
Linear Motion: A force can cause linear motion, while moments or torque relate to the rotational aspects of motion.
Worked Example 2.1.1 - Calculating Torque
Problem Statement: A bus driver applies a force of 45.0 N on the steering wheel as it turns a right-hand corner. The radius of the steering wheel is 30.0 cm. The force is applied at 90.0° to the radius.
Calculation:
Torque (t) can be calculated as:
t = rF ext{ sin}(90^ ext{o})
= 0.30 imes 45.0 ext{ N} = 13.5 ext{ N·m}.
Worked Example 2.1.2 - Calculating Perpendicular Distance
Problem Statement: A car driver can apply a maximum force of 845 N on a wheel-nut spanner, adjustable up to 30.0 cm in length. The force is applied at 90.0° to the radius. The wheel nuts need a torque of 224 N·m to remove them.
Calculation:
Required length of the spanner can be calculated from:
224 ext{ N·m} = r imes 845 ext{ N}.Therefore,
r = rac{224 ext{ N·m}}{845 ext{ N}}
ightarrow 0.264 ext{ m}.Since 30.0 cm = 0.3 m, the spanner length is sufficient.
Problem of the Door
Problem Statement: Door width = 90 cm. Calculate moments for each force about the hinge:
(i) 180 N at 3 cm from the hinge:
Using t = rF for door problem leads to the moment value calculation.
(ii) 225 N downward at 45°, 4 cm from hinge:
(iii) 150 N at the right edge:
Opening a Lid Problem
Question: In which direction does the finger's force have to act? Why?
Frictional Force: Determine the minimum frictional force required between the lid and the edge of the tin can to keep it stable.
Worked Example 2.1.3 - Calculating Torque from Perpendicular Component of Force
Problem Statement: A student uses a 42.0 cm long adjustable spanner to loosen a nut on their bike, applying a force of 65.0 N at an angle of 68.0° to the spanner.
Calculation:
t = rF ext{ sin}( heta).
Using:
t = 0.42 imes 65 imes ext{sin}(68.0^ ext{o})The anticlockwise torque can be solved from the equation.
Worked Example 2.1.4 - Calculating Torque from Perpendicular Component of Distance
Problem Statement: A mechanic uses a 17.0 cm long spanner to tighten a nut on a winch with a force of 104 N applied at 75.0°.
Calculation:
Calculate the clockwise torque using the same principles established above, confirming to three significant figures.
Summary
Key learnings include understanding torque as a key factor in rotational mechanics, correctly calculating moments, determining stability conditions, and applying these concepts to practical scenarios such as vehicles and everyday tools.