# Worksheet: Moments 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 .

Q2:

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 .

Q3:

The force is acting at the point , where the moment about the point is 8 moment units (taking the direction anti-clockwise as 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

Q4:

is a right 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 .

• A 31 Nβcm
• B 21 Nβcm
• C 264 Nβcm
• D 48 Nβcm

Q5:

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.

• A 10 Nβcm
• B 20 Nβcm
• C 95 Nβcm
• D 190 Nβcm

Q6:

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 Nβm,
• B Nβm,
• C Nβm,
• D Nβm,
• E Nβ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:

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

Q9:

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 .

Q10:

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 Nβcm in the direction of , determine the length of .

Q11:

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 triangleβs medians, rounded to two decimal places.

Q12:

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 .

Q13:

is a rhombus having a side length 4 cm in which . Forces of magnitudes 5 N, 10 N, 3 N, N, and 3 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 .

Q14:

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

• A
• B
• C
• D

Q15:

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

Q16:

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

Q17:

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

• A N
• B N
• C N
• D N

Q18:

Determine the moment of the force having a magnitude of 11 N about point . Give your answer in .

Q19:

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.

Q20:

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

Q21:

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.

• A 110 Nβm
• B 315 Nβm
• C 265 Nβm
• D 160 Nβm

Q22:

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 Nβcm, determine the angle between the force of magnitude N and .

• A
• B
• C
• D

Q23:

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

Q24:

In the figure, determine the sum of the moments of the forces 18 N, 11 N, and 3 N about rounding your answer to two decimal places.

Q25:

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 .