Moments

边玩边学

回答这些题目来赚取能量，然后钓鱼探索。无需账号。

给老师：面向 Moments（Physics，CIE）的即用型课程幻灯片, 复习笔记——用在你的课堂上，或将该知识点作为学生可实时游玩的互动课堂活动来运行。

课程笔记

Moments

A moment is the turning effect of a force about a pivot.
Examples: see-saw, spanner, door, crane, screwdriver, tap, wheelbarrow, scissors.
Rotation can be clockwise or anticlockwise (use clock hands as reference).
Equation: moment = force × perpendicular distance from pivot (M = F × d).
Units: newton metre (N m) or newton centimetre (N cm).
Increasing distance from pivot reduces the force needed for the same moment.

Illustration of a pivot and a force acting on a lever, demonstrating a moment.

Principle of Moments (Core)

Principle of moments: For a balanced object, total clockwise moment equals total anticlockwise moment.
Clockwise moment = anticlockwise moment.
Used to solve for unknown forces or distances when the system is in equilibrium.
Always convert distances to metres unless question specifies N cm.

Principle of moments: a beam balanced on a pivot, with the clockwise and anticlockwise turning directions labelled on each side.

Principle of Moments (Extended)

Extended tier: multiple forces on each side of the pivot.
Sum of clockwise moments = sum of anticlockwise moments.
Example: F2 × d2 = (F1 × d1) + (F3 × d3).
Ensure all distances are in the same units and directions are correctly identified.

Three forces on a beam about a pivot, with each force's perpendicular distance from the pivot labelled (d1, d2, d3).

Equilibrium

Equilibrium means a state of balance or stability – no resultant force and no resultant moment.
Conditions: (1) forces balanced (resultant force = 0), (2) clockwise moments = anticlockwise moments (resultant moment = 0).
If either condition fails, the object will accelerate or rotate.

A car with balanced forces at constant speed, and a seesaw with balanced moments, illustrating equilibrium.

Centre of Gravity

Centre of gravity is the point through which the weight of an object acts.
For symmetrical objects of uniform density, it lies at the centre of symmetry.
The centre of gravity can lie inside or outside the object.
In force diagrams, always draw weight from the centre of gravity.

Finding the centre of gravity of symmetrical shapes (triangle, ellipse, trapezium, parallelogram) using axes of symmetry.

Stability

An object is stable when its centre of gravity lies above its base.
If the line of action of weight falls outside the base, the object topples.
Stability increases with a low centre of gravity and a wide base.
Tall, narrow objects (e.g., buses) are less stable and topple more easily.

Stability of vehicles on an incline

Investigating Centre of Gravity (Suspension Method)

Aim: find the centre of gravity of an irregularly shaped plane lamina.
Method: punch 3 holes near edges, hang lamina from a clamp, use a plumb line to mark vertical line of weight.
Repeat for each hole – the intersection of the three lines is the centre of gravity.
When suspended, the object settles with its centre of gravity directly below the point of suspension.
Avoid parallax error by viewing plumb line straight on; allow lamina to settle before marking.

The suspension method: an irregular lamina is hung and a plumb line marked from two different suspension points; the lines intersect at the centre of gravity.

Demonstrating Equilibrium (Extended Experiment)

Aim: show no resultant moment for an object in equilibrium.
Use a metre ruler pivoted at its centre, hang unequal masses on cotton loops at different distances.
Adjust distances until ruler is horizontal and balanced.
Calculate anticlockwise moment (m1 × g × d1) and clockwise moment (m2 × g × d2).
Results should show anticlockwise moment = clockwise moment for equilibrium.
Control variables: equal cotton loop lengths, no friction at pivot.

Apparatus for the equilibrium experiment: a metre ruler balanced on an optical pin pivot with masses hung on cotton loops.

幻灯片

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

练习题

免费预览——43 题中的 8 题。注册即可查看全部。

1.What is the moment of a force?
Easy
- AThe turning effect of a force about a pivot
- BThe speed at which a force is applied
- CThe energy transferred by a force
- DThe power output of a force
2.Which of the following is an example of the turning effect of a force?
Easy
- AA child sitting on a see-saw
- BA book resting on a table
- CA ball rolling down a hill
- DA magnet attracting a nail
3.What is the unit of a moment?
Easy
- Anewton metre (N m)
- Bnewton (N)
- Cmetre (m)
- Djoule (J)
4.A force of 10 N acts at a perpendicular distance of 0.5 m from a pivot. What is the moment?
Easy
- A5 N m
- B20 N m
- C0.5 N m
- D10.5 N m
5.A uniform metre rule is balanced at its midpoint. A 2.0 N weight is placed 30 cm from the pivot on the left. Where must a 3.0 N weight be placed on the right to balance the rule?
Medium
- A20 cm from the pivot
- B30 cm from the pivot
- C45 cm from the pivot
- D15 cm from the pivot
6.The principle of moments states that for an object in equilibrium:
Easy
- Atotal clockwise moment = total anticlockwise moment
- Btotal clockwise moment > total anticlockwise moment
- Ctotal clockwise moment < total anticlockwise moment
- Dthe sum of forces is zero
7.An object will topple over when:
Easy
- Aits centre of gravity lies outside its base
- Bits centre of gravity is directly above its base
- Cits base is very wide
- Dits centre of gravity is low
8.Which of the following increases the stability of an object?
Easy
- ALowering its centre of gravity
- BRaising its centre of gravity
- CMaking its base narrower
- DMaking it taller

更多题目

9.In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin. It comes to rest with its centre of gravity:
Easy
- Adirectly below the point of suspension
- Bdirectly above the point of suspension
- Cat the point of suspension
- Dat the geometric centre of the lamina
10.A man uses a spanner to turn a nut. He applies a force of 40 N at a distance of 0.25 m from the pivot. What is the moment?
Easy
- A10 N m
- B160 N m
- C0.25 N m
- D40.25 N m
11.A beam is in equilibrium with three forces: F1 = 10 N at 0.2 m left of pivot (anticlockwise), F2 = 15 N at 0.3 m right of pivot (clockwise), and F3 at 0.1 m left of pivot (anticlockwise). What is the magnitude of F3?
Hard
- A25 N
- B35 N
- C5 N
- D45 N
12.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. If the counterweight is 5000 N, what is the maximum load that can be lifted without toppling?
Medium
- A10000 N
- B2500 N
- C5000 N
- D2000 N
13.A uniform metre rule is balanced horizontally on a pivot at its centre. A 4.0 N weight is placed 20 cm from the pivot on the left side. A 2.0 N weight is placed 30 cm from the pivot on the right side. What is the resultant moment about the pivot?
Medium
- A0.2 N m clockwise
- B0.2 N m anticlockwise
- C1.4 N m clockwise
- D1.4 N m anticlockwise
14.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action of the weight, the student repeats the process with two more holes. The three lines intersect at a point. What does this point represent?
Medium
- Athe centre of gravity of the lamina
- Bthe point of suspension
- Cthe centre of mass of the lamina
- Dthe centre of the lamina
15.In the experiment to demonstrate equilibrium using a metre ruler and masses, which of the following is a control variable?
Medium
- Athe length of the cotton loops on each side of the pivot
- Bthe mass added to the hangers
- Cthe distance of the masses from the pivot
- Dthe moment calculated
16.In the equilibrium experiment using a metre ruler, the ruler is balanced on a pin. One student suggests that friction between the ruler and the pin might affect the results. Which of the following is the best way to reduce this systematic error?
Medium
- Aensure the ruler is perfectly horizontal before adding masses
- Buse a spirit level to check the ruler's angle
- Ccheck that the ruler is free to rotate with no friction
- Duse a G clamp to secure the clamp stand
17.Which of the following is the correct definition of the centre of gravity of an object?
Easy
- Athe point through which the weight of the object acts
- Bthe point at which the object is balanced
- Cthe geometric centre of the object
- Dthe point where the object's mass is concentrated
18.A uniform metre rule is balanced on a pivot at its centre. A 2.0 N weight is placed at the 20 cm mark on the left side. Where should a 3.0 N weight be placed on the right side to balance the rule?
Medium
- A20 cm
- B30 cm
- C40 cm
- D50 cm
19.Which of the following is a unit of moment?
Easy
- Anewton metre
- Bnewton per metre
- Cjoule
- Dwatt
20.In the experiment to find the centre of gravity of an irregular lamina, why is it important to punch the holes before drawing the lines?
Medium
- Ato ensure the holes are at the correct positions
- Bbecause punching holes after can affect the position of the centre of gravity
- Cto make the lamina easier to hang
- Dto avoid parallax error
21.An object will topple over when its centre of gravity:
Easy
- Alies above its base
- Blies outside its base
- Cis at its lowest possible point
- Dis directly above the pivot
22.A uniform metre rule is balanced at its centre. Where is its centre of gravity?
Easy
- AAt the 50 cm mark
- BAt the 0 cm mark
- CAt the 100 cm mark
- DAt the point of suspension
23.A force of 5 N is applied at a perpendicular distance of 20 cm from a pivot. What is the moment in N m?
Easy
- A1.0 N m
- B100 N m
- C0.25 N m
- D25 N m
24.Which of the following describes a system in equilibrium?
Easy
- AThe sum of clockwise moments equals the sum of anticlockwise moments
- BThe forces are balanced but there is a resultant moment
- CThe object is moving at constant velocity
- DThe object is accelerating
25.A uniform beam is balanced on a pivot. A 10 N weight is placed 0.4 m to the left of the pivot. Where must a 5 N weight be placed on the right to balance the beam?
Medium
- A0.8 m from the pivot
- B0.2 m from the pivot
- C0.4 m from the pivot
- D0.6 m from the pivot
26.An object is more stable when its centre of gravity is:
Easy
- Alow and its base is wide
- Bhigh and its base is narrow
- Clow and its base is narrow
- Dhigh and its base is wide
27.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action, what should the student do next?
Medium
- ASuspend the lamina from a different hole and draw another line
- BWeigh the lamina and calculate the centre of gravity
- CMeasure the distance from the hole to the line
- DCut the lamina along the line
28.In an experiment to demonstrate equilibrium, a metre ruler is balanced on a pivot at its centre. A 100 g mass is hung at the 20 cm mark on the left, and a 200 g mass is hung at the 70 cm mark on the right. What is the resultant moment about the pivot? (Take g = 10 N/kg)
Medium
- A0.1 N m clockwise
- B0.1 N m anticlockwise
- C0.3 N m clockwise
- D0.3 N m anticlockwise
29.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action of the weight, the process is repeated from two other holes. Why are three lines drawn?
Medium
- ATo ensure accuracy by finding the intersection point
- BTo measure the weight of the lamina
- CTo check if the lamina is uniform
- DTo determine the area of the lamina
30.A uniform beam of weight 120 N and length 6.0 m is supported at its ends. A load of 80 N is placed 2.0 m from the left end. What is the upward force at the left support?
Hard
- A113.3 N
- B86.7 N
- C60.0 N
- D40.0 N
31.The unit of moment is the newton metre (N m).
Easy
True or false?
32.For an object in equilibrium, the total clockwise moment equals the total anticlockwise moment.
Easy
True or false?
33.The centre of gravity of a symmetrical object of uniform density is at its centre of symmetry.
Easy
True or false?
34.Match each term with its correct description.
Medium
- Moment
- Centre of gravity
- Equilibrium
- Stability
- Turning effect of a force
- Point where weight acts
- State of balanced forces and moments
- Resistance to toppling
35.Arrange the steps to find the centre of gravity of an irregular lamina using the suspension method in the correct order.
Medium
- Punch three holes near the edges of the lamina.
- Suspend the lamina from a clamp using a loop of thread through one hole.
- Use a plumb line to mark the vertical line of action of the weight.
- Repeat with two other holes to draw two more lines.
- The intersection of the three lines is the centre of gravity.
36.Which of the following are conditions for an object to be in equilibrium? (Select all that apply)
Medium
- AThe forces on the object must be balanced.
- BThere must be no resultant force.
- CThe sum of clockwise moments must equal the sum of anticlockwise moments.
- DThe object must be at rest.
- EThe object must be moving at constant speed.
37.A uniform metre rule is pivoted at its centre. A 4.0 N weight is suspended from the rule at the 5 cm mark. The rule is held by a string at the 30 cm mark, as shown in the diagram. The rule is in equilibrium. What is the upward force that the string exerts on the rule?
Hard
- A0.67 N
- B4.0 N
- C6.0 N
- D9.0 N
38.Complete the sentence.
Easy
The moment of a force is calculated by multiplying the force by the ____ distance from the pivot.
39.State the principle of moments.
Easy
40.A force of 30 N is applied perpendicularly to a spanner at a distance of 0.25 m from the pivot. Calculate the moment of the force.
Easy
41.A uniform beam of weight 120 N and length 6.0 m is supported at its ends. A load of 80 N is placed 2.0 m from the left end. Calculate the upward force at the left support.
Hard
42.Explain why a bus is more likely to topple over on a windy day than a car. Use the terms 'centre of gravity' and 'base' in your answer.
Medium
43.A force of 30 N is applied perpendicularly to a spanner at a distance of 0.25 m from the pivot. Calculate the moment of the force.
Easy
- A9.5 N m
- B8.5 N m
- C7.5 N m
- D6.5 N m

Unlock all 43 questions & more

创建免费账号，即可查看该知识点的每一道题、幻灯片、闪卡和复习笔记。

历年真题

该知识点的历年真题练习即将推出。

即将推出