# Worksheet: Moments in 2D

In this worksheet, we will practice finding the sum of moments of a group of forces acting on a body about a point in 2D.

**Q2: **

Given that is a square with side length 7 cm and forces acting on it as shown in the figure, calculate the algebraic sum of the moments about vertex .

**Q3: **

In the figure, determine the sum of the moments of the forces 13 N, 18 N, and 7 N about rounding your answer to two decimal places.

**Q4: **

Determine the moment of the force that has a magnitude of 11 N about point . Give your answer in Nā m.

**Q5: **

In the given figure, determine the moment about point , given that the force 11 is measured in newtons.

**Q6: **

In the given figure, find the magnitude of the sum of the moments about of the forces whose magnitudes are 5 N and 18 N.

- A160 Nā m
- B265 Nā m
- C315 Nā m
- D110 Nā m

**Q7: **

Two forces and are acting at the points and respectively, where and . If the sum of the moments of the forces about the origin point is zero, determine the value of .

**Q8: **

If the force is acting at the point , where the moment of about each of the two points and is , find .

- A
- B
- C
- D

**Q9: **

If the force is acting at the point , determine the moment of about the point .

- A
- B
- C
- D

**Q10: **

End of is at and has midpoint . If the line of action of the force bisects , determine the moment of about point .

**Q11: **

is an isosceles triangle in which and . Forces of 20, 17, and newtons are acting on , , and , respectively. Find the sum of the moments of the forces about the midpoint of , given that the positive direction is .

**Q12: **

Three forces, measured in newtons, are acting along the sides of an equilateral triangle as shown in the figure. Given that the triangle has a side length of 7 cm, determine the algebraic sum of the moments of the forces about the midpoint of rounded to two decimal places.

**Q13: **

is an equilateral triangle, having a side length of 4 cm. Knowing that forces of magnitudes 150 N, 400 N, and 50 N are acting as shown in the figure, determine the sum of the moments of these forces about the point of intersection of the triangleās medians, rounded to two decimal places.

**Q14: **

is a rhombus having a side length 2 cm in which . Forces of magnitudes 2 N, 6 N, 2 N, N, and 4 N are acting along , , , , and , respectively. If the sum of the moments of these forces about equals the sum of moments of the forces about the point of intersection of the two diagonals of the rhombus, find .

**Q15: **

is a rectangle, where and , and forces of magnitudes 24, 30, 8, and 30 newtons are acting along , , , and , respectively. If the point , where the sum of the moments of the forces about is 53 Nā cm in the direction of , determine the length of .

**Q16: **

is a rectangle, where is the midpoint of , , and . Forces of magnitudes 10, 20, and 12 newtons are acting along , , and , respectively, and a force of magnitude N is acting at the point . If the algebraic sum of the moments of the forces about is 160 Nā cm, determine the angle between the force of magnitude N and .

- A
- B
- C
- D

**Q17: **

The force is acting at the point , in parallel to , where the coordinates of the points and are and respectively. Determine the distance between the point and the line of action of .

**Q18: **

The force is acting at the point , where its moment about the point is 8 moment units (taking the direction counterclockwise to be positive) and its moment about the point is equal to zero. Determine the magnitude of .

- A force units
- B force units
- C force units
- D force units

**Q19: **

A force acts at the point . Calculate the moment, , of this force about the origin, and the length of the perpendicular from its line of action to the origin.

- A Nā m,
- B Nā m,
- C Nā m,
- D Nā m,
- E Nā m,

**Q20: **

The force is acting in the plane of a triangle , where , , and . If and , determine the magnitude of .

- A force units
- B force units
- C force units
- D force units

**Q21: **

Given that force acts through the point , determine the moment about the origin of the force . Also, calculate the perpendicular distance between and the line of action of the force.

- A , length units
- B , length units
- C , length units
- D , length units

**Q22: **

A force in the -plane is acting on . If the algebraic measure of the moment of at point equals 63 Nā m, that at point equals Nā m, and that at point equals zero, determine .

- A N
- B N
- C N
- D N

**Q23: **

is a right-angled triangle where , and . , where . Draw to meet at . Given that forces of magnitudes 2, 15, 13, and 9 newtons are acting along , , , and respectively, find the magnitude of the sum of the moments of the forces about .

**Q24: **

A light circular disk has a center and a diameter of 50 cm. Two chords, and , lie on the disk on different sides of with lengths of 30 cm and 40 cm respectively. Two forces, with magnitudes of 10 and 7 newtons, act along and respectively. If a perpendicular axis is fixed through the point , find the sum of the moments about this point given that is the positive direction of rotation.

**Q25: **

is a square of side length 28 cm, where forces of magnitudes 6, 4, , 8, , and newtons are acting along , , , , , and respectively. Determine the value of , given that the sum of the moments about equals that about .