Question

answer each of the following relative to the center of the wheel.
f = 8 unit
r_⊥ = 20 unit
τ = | unit,
(there is a diagram of a wheel with a 10cm grid and an 8n force arrow at the bottom right of the wheel.)

Explanation:

Step1: Recall the torque formula

Torque \(\tau\) is calculated as \(\tau = r_{\perp} \times F\), where \(r_{\perp}\) is the perpendicular distance from the axis (center of the wheel) to the line of action of the force, and \(F\) is the force.
Given \(F = 8\) unit (let's assume the force unit is N) and \(r_{\perp}=20\) unit (let's assume the distance unit is cm, but we can calculate the torque first).

Step2: Calculate torque

Using the formula \(\tau = r_{\perp} \times F\), substitute \(r_{\perp} = 20\) and \(F = 8\).
\(\tau=20\times8 = 160\)
Now, we need to check the units. If \(r_{\perp}\) is in cm and \(F\) is in N, the torque unit would be \(N\cdot cm\), but we can also convert to \(N\cdot m\) by dividing by 100 (since \(1m = 100cm\)), but the problem might just want the numerical value with the product of units. However, from the given, we just calculate the product.

Answer:

\(\tau = 160\) (with units depending on the original units of \(r_{\perp}\) and \(F\), here if \(r_{\perp}\) is in cm and \(F\) in N, it's \(N\cdot cm\) or if we consider standard torque units, maybe convert \(r_{\perp}\) to meters: \(20cm=0.2m\), then \(\tau = 0.2m\times8N = 1.6N\cdot m\), but based on the given numbers, \(20\times8 = 160\) as the product of the given values)