Final answer:
To calculate the magnitude of the torque due to force F3, the correct formula is Torque = Force × Moment Arm, identified as option D. If the angle between the force and the lever arm is zero, there is no torque produced since the sine of zero is zero, resulting in a product of zero.
Step-by-step explanation:
To calculate the magnitude of the torque (denoted by τ or T) due to force F3, we need to use the following formula: T = rF sin θ, where r is the distance from the axis of rotation to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force vector and the lever arm vector. The lever arm vector is perpendicular to the force vector and extends from the axis of rotation to the line of action of the force.
The lever arm (r₁) can also be expressed as r₁ = r sin θ. For torque calculation, it is essential to consider the perpendicular distance (lever arm) from the axis to the force vector. If the angle θ is zero, which means the force is acting along the lever arm and not perpendicular to it, then F3 does not produce any torque, as sin 0 = 0, and thus T = rF sin 0 = 0.
In the provided example where -0.5 m (30 N) equals -15.0 N·m, it shows an example of calculating torque with the force acting perpendicularly to the lever arm since the sin of the angle is not given. For F3 not producing any torque, it indicates that the force is acting in a direction that does not generate a rotational effect on the object or flywheel in question.
In summary, the correct option for calculating the torque due to force F3 is D) Torque = Force × Moment Arm. The units for torque are Newton-meters (N·m), and this quantity plays a pivotal role in understanding rotational dynamics and mechanical advantage in physics.