9th Class Physics Unit No.4 Turning Effect of Forces Notes
The principle of moments states that for a body to be in a state of equilibrium (not rotating), the sum of the clockwise moments acting on the body must be equal to the sum of the anticlockwise moments acting on it.
Consider a body initially at rest, and let us analyze the moments acting on it in different situations:
Clockwise Moments: These are moments produced by forces that tend to rotate the body in the clockwise direction around a fixed axis. For example, when tightening a nut using a spanner in the clockwise direction, a clockwise moment is generated.
- Chapter No.1 Introduction to Biology
- Chapter No. 2 Solving a Biological Problem
- Chapter No.3 Biodiversity
- Chapter No.4 Cells and Tissues
- Chapter No.5 Cell Cycle
Anticlockwise Moments: These are moments produced by forces that tend to rotate the body in the anticlockwise direction around a fixed axis. For example, when loosening a nut using a spanner in the anticlockwise direction, an anticlockwise moment is generated.
For the body to remain in equilibrium (not rotate), the total anticlockwise moments must be balanced by the total clockwise moments. In mathematical terms:
ΣClockwise Moments = ΣAnticlockwise Moments
By following the principle of moments, we can ensure that a body remains at rest without any rotational motion. This concept is crucial in engineering, architecture, and other fields where stability and balance are essential considerations.
The concept of the center of mass is observed when a system’s mass appears concentrated at a single point, and a force applied at this point causes the system to move in the direction of the net force without any rotation. This point is called the center of mass, and it is used to describe the motion of the entire system.
For a system of two particles connected by a rigid rod, the center of mass is the point O between the particles, where an applied force does not cause any rotation, and the system moves as a whole. However, if the force is applied away from the center of mass, the system will not only move but also rotate.
The center of gravity is a point within a body where the entire weight of the body appears to act vertically downward. It is the point where the resultant of all the forces due to gravity acts. For symmetrical objects like a uniform rod, square, rectangular sheet, circular disc, solid or hollow sphere, the center of gravity can be determined geometrically. For irregular shapes, a plumbline can be used to locate the center of gravity.
When a body is in equilibrium, it either remains at rest or moves with a constant velocity. There are two conditions for equilibrium: first, the resultant of all the forces acting on the body must be zero, and second, the resultant torque acting on the body must be zero.
A stable equilibrium is a state where a body, when slightly tilted, returns to its original position. The center of gravity of the body is at its lowest position in stable equilibrium, and the body remains stable as long as the center of gravity stays within its base. For vehicles, a low center of gravity and a wide base are essential for stability during turns.
In contrast, unstable equilibrium occurs when a body, when slightly tilted, moves away from its original position. The center of gravity in this case is at its highest position. Neutral equilibrium refers to a state where a body remains in any position, regardless of slight disturbances. In neutral equilibrium, the center of gravity does not rise or fall when the body is slightly tilted.
Unstable equilibrium is a state in which a body, such as a pencil, cannot maintain its position when slightly tilted. If left unsupported, the body will topple over about its base. The center of gravity of the body is at its highest position in unstable equilibrium, and as the body topples, the center of gravity moves towards its lower position and does not return to its previous position.
Neutral equilibrium refers to a state in which a body remains in its new position when disturbed from its previous position. Objects in neutral equilibrium have all new states as stable states. For example, a ball or a sphere placed on a horizontal surface will remain in its displaced position without returning to its original spot. In neutral equilibrium, the center of gravity of the body remains at the same height regardless of its new position.
Stability and the position of the center of mass are closely related. Objects with stable equilibrium are designed to have their center of mass kept as low as possible. For example, racing cars are made heavy at the bottom to increase stability and prevent toppling. Circus artists, such as tightrope walkers, use long poles to lower their center of mass, which helps maintain their balance and prevent falling. Objects like a perched parrot or a self-righting toy return to their stable states when disturbed, as their center of mass is vertically below their point of support, ensuring stable equilibrium.
How does the head-to-tail rule help to find the resultant of forces?
The head-to-tail rule, also known as the parallelogram law of vector addition, is used to find the resultant of two or more forces acting on a body. To apply this rule, we draw vectors representing each force, placing the tail of each vector at the head of the previous one. The resultant vector is then drawn from the tail of the first vector to the head of the last vector. The magnitude and direction of the resultant vector represent the combined effect of all the forces acting on the body.
How can a force be resolved into its perpendicular components?
A force can be resolved into its perpendicular components using the concept of vector decomposition. When a force acts at an angle to a given axis, it can be split into two components: one along the axis and the other perpendicular to it. These components are obtained by using trigonometric functions, such as sine and cosine. The component along the axis is given by Fx = F * cosθ, and the component perpendicular to the axis is given by Fy = F * sinθ, where F is the magnitude of the force, and θ is the angle it makes with the axis.
When is a body said to be in equilibrium?
A body is said to be in equilibrium when it is either at rest or moving with constant velocity in a straight line. In equilibrium, the net force acting on the body is zero, which means the vector sum of all the forces acting on the body is balanced, resulting in no acceleration. There are two conditions for equilibrium: the first condition deals with the forces being balanced, and the second condition deals with the torques (rotational forces) being balanced.
Explain the first condition for equilibrium.
The first condition for equilibrium states that a body will be in equilibrium if the vector sum of all the forces acting on it is zero. Mathematically, this can be expressed as ∑F = 0, where ∑F represents the vector sum of all the forces acting on the body. When the forces are balanced, the body will not experience any linear acceleration and will remain either at rest or move with constant velocity.
Why is there a need for the second condition for equilibrium if a body satisfies the first condition for equilibrium?
While the first condition deals with the balance of forces, it does not guarantee equilibrium in all cases. A body can still be rotating or experiencing angular acceleration even if the linear forces are balanced. The second condition for equilibrium addresses this aspect and states that a body will be in equilibrium if the vector sum of all the torques acting on it is zero. This condition ensures that the body is not only in translational equilibrium (balance of linear forces) but also in rotational equilibrium (balance of rotational forces). Mathematically, this can be expressed as ∑τ = 0, where ∑τ represents the vector sum of all the torques acting on the body.
What is the second condition for equilibrium?
The second condition for equilibrium states that a body will be in equilibrium if the vector sum of all the torques acting on it is zero. In other words, the net torque acting on the body must be balanced, leading to no angular acceleration. This condition ensures that the body is not only in translational equilibrium (balance of linear forces) but also in rotational equilibrium (balance of rotational forces).
Give an example of a moving body that is in equilibrium.
An example of a moving body that is in equilibrium is a car moving at a constant velocity along a straight road with no acceleration. In this case, the forces acting on the car, such as the driving force and the frictional force, are balanced, resulting in translational equilibrium. Additionally, if there are no rotational forces acting on the car, such as no turning or steering, the car will also be in rotational equilibrium.
Think of a body that is at rest but not in equilibrium.
An example of a body at rest but not in equilibrium is a book placed on the edge of a table without falling. While the book is not moving, it is not in equilibrium because the gravitational force is unbalanced. The book is being acted upon by the force of gravity pulling it downward, but the table exerts an equal and opposite normal force, preventing it from falling. The book is stable in its position, but it is not in equilibrium as the forces are unbalanced.
Why can a body not be in equilibrium due to a single force acting on it?
A body cannot be in equilibrium due to a single force acting on it because equilibrium requires the vector sum of all forces to be zero. A single force acting on a body will either cause it to accelerate or remain in motion at a constant velocity, depending on whether the force is unbalanced or balanced, respectively. To achieve equilibrium, multiple forces with suitable magnitudes and directions are necessary to cancel out each other’s effects and maintain a state of balance.
Why is the height of vehicles kept as low as possible?
The height of vehicles is kept as low as possible to increase their stability. When the center of mass of a vehicle is low, it becomes less prone to toppling over during turns or maneuvers. This is particularly important for vehicles with high speeds or tight turns. Lowering the center of mass reduces the chances of the vehicle losing its balance and helps to prevent accidents.
Explain what is meant by stable, unstable, and neutral equilibrium. Give one example in each case.
Stable equilibrium: A body is in stable equilibrium when it returns to its original position after being slightly displaced and then released. In this state, the center of gravity is at its lowest position, ensuring that the body remains balanced and returns to its stable state. An example of stable equilibrium is a ball placed in a concave surface.
Unstable equilibrium: A body is in unstable equilibrium when it cannot maintain its position after being slightly displaced and then released. In this state, the center of gravity is at its highest position, and the body topples over about its base. An example of unstable equilibrium is a pencil standing vertically on its tip.
Neutral equilibrium: A body is in neutral equilibrium when it remains in its new position after being slightly displaced and then released. In this state, the center of gravity remains at the same height regardless of its new position, and the body does not return to its previous state. An example of neutral equilibrium is a ball placed on a flat surface.