What is the magnitude of torque resulting from a 2.4 N force applied 17 cm from the point of rotation, if the force is applied perpendicular to the displacement vector?

To find the magnitude of torque when a force is applied perpendicular to the displacement vector, you can use the formula for torque, which is given by:

[

\tau = r \times F

]

where ( \tau ) is the torque, ( r ) is the distance from the point of rotation to the point where the force is applied (lever arm), and ( F ) is the applied force. When the force is perpendicular to the lever arm, the angle (\theta) between the force vector and the lever arm is 90 degrees, and therefore (\sin(\theta) = 1).

First, convert the distance from centimeters to meters for consistency in units. Since 1 cm is equal to 0.01 m, 17 cm is:

[

17 , \text{cm} = 0.17 , \text{m}

]

Now, substituting the values into the torque formula:

[

\tau = 0.17 , \text{m} \times 2.4 , \text{N}

]

Calculating this gives:

[

\tau = 0.408 , \text{N m}

\