Torque, Basic Introduction, Lever Arm, Moment of Force, Simple Machines & Mechanical Advantage

Summary

The video introduces torque, also called the moment of force, and explains how it describes a force’s tendency to rotate an object. It then applies torque to simple machines, showing how leverage can increase output force.

Torque and lever arm

A door is easier to push near its outer edge than near its hinges, even when the applied force is the same. The difference is the lever arm: applying force farther from the axis of rotation produces more torque.

Torque is calculated as:

• τ = F × r, where r is the moment arm.
• The moment arm is the perpendicular distance from the axis of rotation to the force’s line of action.

When a force is applied at an angle, torque can be calculated in either of these equivalent ways:

• τ = F × l × sin θ, where l is the distance from the axis to the point where the force is applied, and θ is the angle between the force and that distance.
• τ = F⊥ × l, where F⊥ = F sin θ is the component of the force perpendicular to the object.

A force directed along the object produces little or no turning effect; the perpendicular component creates the torque.

Torque direction and net torque

The video uses the following sign convention:

• Counterclockwise torque is positive.
• Clockwise torque is negative.

To find net torque, calculate each force’s torque with its direction sign, then add the results.

Example: A 200 N force applied 3 m from an axis creates +600 N·m. A 400 N force applied 1.5 m away in the clockwise direction creates −600 N·m. The net torque is zero, so the torques balance.

Propeller example: The three torques are approximately −1,200 N·m, +1,558.8 N·m, and +1,915.1 N·m. Their sum is about +2,274 N·m, so the net tendency is to rotate counterclockwise.

Leverage and mechanical advantage

A simple machine can use a longer input lever arm to produce a larger output force at a shorter lever arm. For the seesaw and shovel examples, the input and output torques balance:

Finput × Linput = Foutput × Loutput

Mechanical advantage (MA) is the ratio of output force to input force:

MA = Foutput / Finput

For an ideal lever, the ideal mechanical advantage (IMA) is also:

IMA = input lever arm / output lever arm

Actual machines may provide less force than the ideal calculation predicts.

Simple-machine examples

• Seesaw: Applying 300 N at a 6 m input arm creates 1,800 N·m of torque. With a 3 m output arm, the balanced output force is 600 N. The mechanical advantage is 2.
• Shovel: With a 200 N input force applied 1 m from the axis and an output arm of 0.1 m, the output force is 2,000 N. The mechanical advantage is 10.

The shovel example illustrates that the longer arm corresponds to the smaller applied force, while the shorter arm can produce a larger output force. Moving the hand closer to the axis shortens the input lever arm and reduces mechanical advantage. For lifting with less effort, the instructor recommends placing the hand at the shovel’s far end, though this may require moving it through a greater distance.

Speaker and source

• The Organic Chemistry Tutor — the video’s instructor and sole speaking source in the subtitles.