Question

Four forces are exerted on a disk of radius R that is free to spin about its center, as shown above. The magnitudes are proportional to the length of the force vectors, where F1 = F4, F2 = F3 , and F1 = 2F2. Which two forces combine to exert zero net torque on the disk? Select two answers.
(A) F1
(B) F2
(C) F3
(D) F4

Answer 1

The given magnitude of forces of F₁ = F₄, F₂ = F₃, F₁ = 2·F₂, give the

forces that exert zero net torque on the disk as the options;

(B) F₂

(D) F₄

How can the net torque on the disk be calculated?

The given parameters are;

F₁ = F₄

F₂ = F₃

F₁ = 2·F₂

Therefore;

F₄ = 2·F₂

In vector form, we have;

$\vec{F_4} = \mathbf{\frac{\sqrt{3} }{2} \cdot F_4 \cdot \hat i - 0.5 \cdot F_4 \hat j}$

$\vec{F_2} = \mathbf{ -F_2 \, \hat j}$

Clockwise moment due to F₄, M₁ = $-0.5 \times F_4 \, \hat j \times \dfrac{R}{2}$

Therefore;

$M_1 =- 0.5 \times 2 \times F_2 \, \hat j \times \dfrac{R}{2} = \mathbf{ -F_2 \, \hat j \times \dfrac{R}{2}}$

Counterclockwise moment due to F₂ = $-F_2 \, \hat j \times \dfrac{R}{2}$

Given that the clockwise moment due to F₄ = The counterclockwise moment due to F₂, we have;

Two forces that combine to exert zero net torque on the disk are;

F₂, and F₄

Which are the options; (B) F₂, and (D) F₄

Learn more about the resolution of vectors here:

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