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Lesson: Moments in 2D

Sample Question Videos

Worksheet • 25 Questions • 1 Video

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 N m β‹… .

Q2:

The force F i j = 3 + π‘š is acting at the point 𝐴 ( βˆ’ 5 , βˆ’ 4 ) , in parallel to  𝐡 𝐷 , 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 .

Q3:

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

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

Q4:

𝐴 𝐡 𝐢 is a right-angled triangle where π‘š ∠ 𝐡 = 9 0 ∘ , 𝐴 𝐡 = 2 0 c m and 𝐴 𝐢 = 2 5 c m . 𝐷 ∈ 𝐴 𝐢 , where 𝐴 𝐷 = 4 c m . Draw 𝐷 𝐸 βŸ‚ 𝐴 𝐢 to meet 𝐴 𝐡 at 𝐸 . Given that forces of magnitudes 2, 15, 13, and 9 newtons are acting along  𝐴 𝐡 , οƒͺ 𝐡 𝐢 ,  𝐴 𝐢 , and  𝐷 𝐸 respectively, find the magnitude of the sum of the moments of the forces about 𝐡 .

Q5:

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

Q6:

A force ⃑ 𝐹 = 4 ⃑ 𝑖 + 1 2 ⃑ 𝑗 N acts at the point 𝐴 ( βˆ’ 4 , βˆ’ 1 ) m . Calculate the moment, 𝑀 π‘œ , 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 ⃑ π‘˜ π‘œ Nβ‹…m, 𝐿 = 1 1 √ 1 0 1 0 m
  • B 𝑀 = βˆ’ 5 2 ⃑ π‘˜ π‘œ Nβ‹…m, 𝐿 = 1 3 √ 1 0 1 0 m
  • C 𝑀 = βˆ’ 2 8 ⃑ π‘˜ π‘œ Nβ‹…m, 𝐿 = 7 √ 1 0 1 0 m
  • D 𝑀 = βˆ’ 2 8 ⃑ π‘˜ π‘œ Nβ‹…m, 𝐿 = 7 4 m
  • E 𝑀 = βˆ’ 4 4 ⃑ π‘˜ π‘œ Nβ‹…m, 𝐿 = 1 1 4 m

Q7:

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

Q8:

The force ⃑ 𝐹 is acting in the plane of a triangle 𝐴 𝐡 𝐢 , where 𝐴 ( 3 , 1 ) , 𝐡 ( 6 , 6 ) , and 𝐢 ( 7 , 2 ) . If οƒ  𝑀 = οƒ  𝑀 = 3 4 ⃑ π‘˜ 𝐴 𝐡 and 𝑀 = βˆ’ 3 4 ⃑ π‘˜ 𝐢 , determine the magnitude of ⃑ 𝐹 .

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

Q9:

𝐴 𝐡 𝐢 is an isosceles triangle in which π‘š ∠ 𝐡 = 1 2 0 ∘ and 𝐴 𝐢 = 1 2 0 √ 3 c m . Forces of 20, 17, and 1 4 √ 3 newtons are acting on  𝐴 𝐢 , οƒͺ 𝐢 𝐡 , and  𝐴 𝐡 , respectively. Find the sum of the moments of the forces about the midpoint of 𝐡 𝐢 , given that the positive direction is 𝐢 𝐡 𝐴 .

Q10:

𝐴 𝐡 𝐢 𝐷 is a rectangle, where 𝐴 𝐡 = 6 c m and 𝐡 𝐢 = 8 c m , and forces of magnitudes 24, 30, 8, and 30 newtons are acting along  𝐡 𝐴 , οƒͺ 𝐡 𝐢 ,  𝐢 𝐷 , and  𝐢 𝐴 , respectively. If the point 𝐸 ∈ 𝐡 𝐢 , where the sum of the moments of the forces about 𝐸 is 53 Nβ‹…cm in the direction of 𝐴 𝐡 𝐢 𝐷 , determine the length of 𝐡 𝐸 .

Q11:

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.

Q12:

𝐴 𝐡 𝐢 𝐷 is a rhombus having a side length 2 cm in which π‘š ∠ 𝐴 𝐡 𝐢 = 6 0 ∘ . Forces of magnitudes 2 N, 6 N, 2 N, 𝐹 N, and 4 N are acting along  𝐡 𝐴 , οƒͺ 𝐢 𝐡 ,  𝐢 𝐷 ,  𝐴 𝐷 , and  𝐴 𝐢 , 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 .

Q13:

𝐴 𝐡 𝐢 𝐷 is a rhombus having a side length 4 cm in which π‘š ∠ 𝐴 𝐡 𝐢 = 6 0 ∘ . Forces of magnitudes 5 N, 10 N, 3 N, 𝐹 N, and 3 N are acting along  𝐡 𝐴 , οƒͺ 𝐢 𝐡 ,  𝐢 𝐷 ,  𝐴 𝐷 , and  𝐴 𝐢 , 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 .

Q14:

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

  • A 2 5 ⃑ π‘˜
  • B βˆ’ 7 0 ⃑ π‘˜
  • C 7 0 ⃑ π‘˜
  • D βˆ’ 2 5 ⃑ π‘˜

Q15:

Given that force ⃑ 𝐹 = 4 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 acts through the point 𝐴 ( 3 , 6 ) , determine the moment οƒŸ 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 οƒŸ 𝑀 = βˆ’ 3 3 ⃑ π‘˜ , 𝐿 = 6 . 6 length units
  • B οƒŸ 𝑀 = 1 5 ⃑ π‘˜ , 𝐿 = 3 length units
  • C οƒŸ 𝑀 = βˆ’ 1 5 ⃑ π‘˜ , 𝐿 = 3 length units
  • D οƒŸ 𝑀 = 3 ⃑ π‘˜ , 𝐿 = 6 . 6 length units

Q16:

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

Q17:

A force ⃑ 𝐹 in the π‘₯ 𝑦 -plane is acting on β–³ 𝐴 𝑂 𝐡 . If the algebraic measure of the moment of ⃑ 𝐹 at point 𝑂 equals 63 Nβ‹…m, that at point 𝐴 equals βˆ’ 1 1 9 Nβ‹…m, and that at point 𝐡 equals zero, determine ⃑ 𝐹 .

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

Q18:

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

Q19:

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

Q20:

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

Q21:

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.

  • A 160 Nβ‹…m
  • B 315 Nβ‹…m
  • C 265 Nβ‹…m
  • D 110 Nβ‹…m

Q22:

𝐴 𝐡 𝐢 𝐷 is a rectangle, where 𝑀 is the midpoint of 𝐡 𝐢 , 𝐴 𝐡 = 1 6 c m , and 𝐡 𝐢 = 1 2 c m . Forces of magnitudes 10, 20, and 12 newtons are acting along  𝐷 𝐴 ,  𝐴 𝐢 , and  𝐢 𝐷 , 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 𝐡 𝐢 .

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

Q23:

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’ 2 8 ⃑ π‘˜ , find ⃑ 𝐹 .

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

Q24:

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

Q25:

Given that 𝐴 𝐡 𝐢 𝐷 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 .

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