The Better Handle

Classical Mechanics Level 1

You want to loosen a stubbornly tight screw, and have two different handles available for the screwdriver.

If you apply the same force to both handles below, which handle is easier to turn the screw with? In other words, which handle will generate a greater turning moment for the screw?

A B Both handles will make the same moment

2 solutions

Tom Engelsman
Feb 3, 2017

Using $\mathbf{r} \times \mathbf{F}$ to calculate our torque moment, one can see it is directly proportional to both the length of the moment arm and the applied force.
If the force is the same in both cases, the torque driver $\textbf{A}$ will generate a larger moment as $r_A > r_B.$

Moderator note:

Like Tom said, the computation suggests $r_AF_A = r_BF_B,$ though on first appearances the definition of torque is a bit opaque.

If $\mathbf{r}\times\mathbf{F}$ doesn't click, we can take a step back and think about things from first principles. Regardless of where the force is applied along the radius, some amount of work must be done to overcome the friction between the screw and whatever it's screwed into.

Let's call this work $W_\textrm{unscrew}.$ Then it must be the case that $W_\textrm{unscrew}$ is equal to $F(r)\cdot\textrm{path length(r)} = F(r)\cdot 2\pi r,$ regardless of the value of $r$ at which we apply the force. Therefore the product $rF$ is a constant.

That's right! If we apply the same force to both screwdrivers, than (A) will generate a larger torque because its distance from the axis is greater.

It is important to take into consideration the correct distance. Having a greater length along the screwdriver won't help as much as having a greater length perpendicular to the axis.

Pranshu Gaba - 4 years, 3 months ago

Dan Barker
Feb 11, 2017

One word... Leverage.... Common sense more than maths for me!

We often have an intuitive feel about how levers work, and how increasing the distance of force from the axis increases the turning moment. We observe this all around us: we open doors by pushing furthest from the hinges. Wheel barrows and nut crackers also work using the same principle.

Pranshu Gaba - 4 years, 3 months ago

I was just thinking about that can barker... but there is one problem. So many questions I've seen where people try to use common sense... and you wounder what is wrong with people on some, and others common sense is where you go wrong.

- 3 years, 7 months ago

Also, the 1st one has a handle that is easier to grab

alex wang - 3 years, 4 months ago

I also feel the same :)

Bibhor Singh - 3 years, 2 months ago

The Better Handle

2 solutions

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