# 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.

Q1:

If a force, having a magnitude of 498 N, is 8 cm away from a point , find the norm of the moment of the force about the point , giving your answer in N⋅m.

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 N⋅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. 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 .

• A
• B
• C
• D

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 triangle’s 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 N⋅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 N⋅cm, determine the angle between the force of magnitude N and . 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 N⋅m,
• B N⋅m,
• C N⋅m,
• D N⋅m,
• E N⋅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 N⋅m, that at point equals N⋅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 .