Question

How does the magnitude of the lever arm will change if you decrease the angle?

It decreases.
It stays the same.
It increases.

Answer 1

Answer: It decreases.

Step-by-step explanation:

Lever arm is defined as the "perpendicular distance that exists from the rotation axis to the line of action of the force". Being its magnitude
`(Nm)` related to the application of the force that produces a torque.

To understand it better:

The lever arm is an effective distance to apply a force with respect to a certain point, and this distance serves as an effective applied force amplification factor.

In this sense, Torque
`\tau` is defined as:

`\tau=rFsin \theta`

Where:

`r` is the distance from the applied force to the fulcrum

`F` is the applied force

`\theta` is the angle between
`r` and
`F`

It is important to note,
`\tau` is maximum when
`\theta=90\°`. Then, assuming
`r` and
`F` remains the same, if
`\theta` decreases
`\tau` decreases, as well.

Hence:

If the angle
`\theta` decreases, the magnitude of the lever arm will decrease.

So, the greater the lever arm, the greater the torque and the lesser the force we have to apply.