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 𝐴, find the norm of the moment of the force about the point 𝐴, giving your answer in Nβ‹…m.

Q2:

Given that 𝐴𝐡𝐢𝐷 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 𝐡.

Q3:

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

Q4:

Determine the moment of the force that has a magnitude of 11 N about point 𝑂. Give your answer in Nβ‹…m.

Q5:

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

Q6:

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

  • A160 Nβ‹…m
  • B265 Nβ‹…m
  • C315 Nβ‹…m
  • D110 Nβ‹…m

Q7:

Two forces F and F are acting at the points 𝐴(4,1) and 𝐡(3,βˆ’1) respectively, where Fij=3βˆ’ and Fij=π‘š+2. If the sum of the moments of the forces about the origin point is zero, determine the value of π‘š.

Q8:

If the force F is acting at the point 𝐴(5,0), where the moment of F about each of the two points 𝐡(1,βˆ’6) and 𝐢(1,9) is βˆ’28k, find F.

  • A βˆ’ 7 j
  • B βˆ’ i
  • C βˆ’ βˆ’ i j
  • D βˆ’ + 2 i j

Q9:

If the force Fij=βˆ’5+π‘š is acting at the point 𝐴(7,3), determine the moment of F about the point 𝐡(7,βˆ’2).

  • A 2 5 k
  • B 7 0 k
  • C βˆ’ 2 5 k
  • D βˆ’ 7 0 k

Q10:

End 𝐴 of 𝐴𝐡 is at (βˆ’6,7) and 𝐴𝐡 has midpoint 𝐷(βˆ’7,1). If the line of action of the force Fij=βˆ’2βˆ’6 bisects 𝐴𝐡, determine the moment of F about point 𝐡.

Q11:

𝐴 𝐡 𝐢 is an isosceles triangle in which π‘šβˆ π΅=120∘ and 𝐴𝐢=120√3cm. Forces of 20, 17, and 14√3 newtons are acting on 𝐴𝐢, οƒͺ𝐢𝐡, and 𝐴𝐡, respectively. Find the sum of the moments of the forces about the midpoint of 𝐡𝐢, given that the positive direction is 𝐢𝐡𝐴.

Q12:

Three forces, measured in newtons, are acting along the sides of an equilateral triangle 𝐴𝐡𝐢 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 𝐴𝐡 rounded to two decimal places.

Q13:

𝐴 𝐡 𝐢 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:

𝐴 𝐡 𝐢 𝐷 is a rhombus having a side length 2 cm in which π‘šβˆ π΄π΅πΆ=60∘. Forces of magnitudes 2 N, 6 N, 2 N, 𝐹 N, and 4 N are acting along 𝐡𝐴, οƒͺ𝐢𝐡, 𝐢𝐷, 𝐴𝐷, and 𝐴𝐢, respectively. If the sum of the moments of these forces about 𝐷 equals the sum of moments of the forces about the point of intersection of the two diagonals of the rhombus, find 𝐹.

Q15:

𝐴 𝐡 𝐢 𝐷 is a rectangle, where 𝐴𝐡=6cm and 𝐡𝐢=8cm, and forces of magnitudes 24, 30, 8, and 30 newtons are acting along 𝐡𝐴, οƒͺ𝐡𝐢, 𝐢𝐷, and 𝐢𝐴, respectively. If the point 𝐸∈𝐡𝐢, where the sum of the moments of the forces about 𝐸 is 53 Nβ‹…cm in the direction of 𝐴𝐡𝐢𝐷, determine the length of 𝐡𝐸.

Q16:

𝐴 𝐡 𝐢 𝐷 is a rectangle, where 𝑀 is the midpoint of 𝐡𝐢, 𝐴𝐡=16cm, and 𝐡𝐢=12cm. Forces of magnitudes 10, 20, and 12 newtons are acting along 𝐷𝐴, 𝐴𝐢, and 𝐢𝐷, respectively, and a force of magnitude 8√2 N is acting at the point 𝑀. If the algebraic sum of the moments of the forces about 𝐡 is 160 Nβ‹…cm, determine the angle between the force of magnitude 8√2 N and 𝐡𝐢.

  • A 4 5 ∘
  • B 9 0 ∘
  • C 6 0 ∘
  • D 3 0 ∘

Q17:

The force Fij=3+π‘š is acting at the point 𝐴(βˆ’5,βˆ’4), in parallel to 𝐡𝐷, where the coordinates of the points 𝐡 and 𝐷 are (5,6) and (9,3) respectively. Determine the distance between the point 𝐡 and the line of action of F.

Q18:

The force F is acting at the point 𝐴(βˆ’4,7), where its moment about the point 𝐡(2,βˆ’1) is 8 moment units (taking the direction counterclockwise to be positive) and its moment about the point 𝐢(3,βˆ’3) is equal to zero. Determine the magnitude of F.

  • A 4 √ 1 7 force units
  • B 2 √ 2 force units
  • C 2 √ 1 4 9 force units
  • D √ 1 7 force units

Q19:

A force Fij=4+12N acts at the point 𝐴(βˆ’4,βˆ’1)m. Calculate the moment, 𝑀, of this force about the origin, and the length of the perpendicular 𝐿 from its line of action to the origin.

  • A 𝑀 = βˆ’ 4 4  k Nβ‹…m, 𝐿 = 1 1 √ 1 0 1 0 m
  • B 𝑀 = βˆ’ 5 2  k Nβ‹…m, 𝐿 = 1 3 √ 1 0 1 0 m
  • C 𝑀 = βˆ’ 4 4  k Nβ‹…m, 𝐿 = 1 1 4 m
  • D 𝑀 = βˆ’ 2 8  k Nβ‹…m, 𝐿 = 7 √ 1 0 1 0 m
  • E 𝑀 = βˆ’ 2 8  k Nβ‹…m, 𝐿 = 7 4 m

Q20:

The force F is acting in the plane of a triangle 𝐴𝐡𝐢, where 𝐴(3,1), 𝐡(6,6), and 𝐢(7,2). If 𝑀=𝑀=34k and 𝑀=βˆ’34k, determine the magnitude of F.

  • A 2 √ 1 5 8 force units
  • B √ 3 0 force units
  • C √ 7 force units
  • D 4 √ 3 4 force units

Q21:

Given that force Fij=4βˆ’3 acts through the point 𝐴(3,6), determine the moment M about the origin 𝑂 of the force F. Also, calculate the perpendicular distance 𝐿 between 𝑂 and the line of action of the force.

  • A M k = 3 , 𝐿 = 6 . 6 length units
  • B M k = βˆ’ 1 5 , 𝐿 = 3 length units
  • C M k = βˆ’ 3 3 , 𝐿 = 6 . 6 length units
  • D M k = 1 5 , 𝐿 = 3 length units

Q22:

A force F in the π‘₯𝑦-plane is acting on △𝐴𝑂𝐡. If the algebraic measure of the moment of F at point 𝑂 equals 63 Nβ‹…m, that at point 𝐴 equals βˆ’119 Nβ‹…m, and that at point 𝐡 equals zero, determine F.

  • A 7 βˆ’ 2 6 i j N
  • B βˆ’ 2 6 βˆ’ 7 i j N
  • C 7 + 2 6 i j N
  • D βˆ’ 2 6 + 7 i j N

Q23:

𝐴 𝐡 𝐢 is a right-angled triangle where π‘šβˆ π΅=90∘, 𝐴𝐡=20cm and 𝐴𝐢=25cm. 𝐷∈𝐴𝐢, where 𝐴𝐷=4cm. Draw π·πΈβŸ‚π΄πΆ to meet 𝐴𝐡 at 𝐸. Given that forces of magnitudes 2, 15, 13, and 9 newtons are acting along 𝐴𝐡, οƒͺ𝐡𝐢, 𝐴𝐢, and 𝐷𝐸 respectively, find the magnitude of the sum of the moments of the forces about 𝐡.

Q24:

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

Q25:

𝐴 𝐡 𝐢 𝐷 is a square of side length 28 cm, where forces of magnitudes 6, 4, 𝐾, 8, 10√2, and 8√2 newtons are acting along 𝐴𝐡, οƒͺ𝐢𝐡, 𝐢𝐷, 𝐴𝐷, 𝐴𝐢, and 𝐷𝐡 respectively. Determine the value of 𝐾, given that the sum of the moments about 𝐡 equals that about 𝐢.

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