Punjab 9th Physics Ch 4 Turning Effect of Force Short Questions

**Like Parallel Forces:** If the parallel forces are acting in the same direction, then they are called like parallel forces. The resultant of like parallel forces is equal to the sum of the magnitudes of all the forces and acts in the same direction as the individual forces.
Example: Two people pushing a car in the same direction.

**Unlike Parallel Forces:** If the parallel forces are acting in the opposite direction, then they are called unlike parallel forces. The resultant of unlike parallel forces is the difference between the magnitudes of the forces and acts in the direction of the larger force.
Example: Two people pushing a table from opposite sides with unequal forces.

The components of a force which are mutually perpendicular to each other are called rectangular components.

• Horizontal component: Fx = Fcosθ
• Vertical component: Fy = Fsinθ

The line along which the force acts is called the line of action of the force. It represents the direction and path of the force and passes through the point of application of the force.

**Moment Arm:** The perpendicular distance from the axis of rotation to the line of action of the force is known as the moment arm. A larger moment arm results in a greater turning effect.

**Proof τ = rFsinθ:**
Torque is the cross product of the force and the perpendicular distance from the axis of rotation to the line of action of the force:
τ = rFsinθ

This shows that the moment of a force depends on the magnitude of the force, the distance r, and the angle θ between r and F.

The perpendicular distance from the axis to the line of action of the force is d = rsinθ. Thus, the torque is:
τ = F × d = F × (rsinθ)

(a) Stable equilibrium
(b) Unstable equilibrium
(c) Neutral equilibrium

A paratrooper coming down with terminal velocity is in equilibrium because his weight in downward direction is equal to the force of air friction of air in upward direction. Paratrooper is moving with uniform velocity, so the paratrooper is in equilibrium.

A car moving with uniform velocity on levelled road is the example of equilibrium.

**Center of Mass:** “The center of mass of a body is that point where the whole mass of the body is assumed to be concentrated.” A force applied at such a point in the body does not produce any torque in it.

**Centre of Gravity:** “Centre of gravity is that point where total weight of the body appears to be acting vertically downward.” If a body is supported at its center of gravity, it remains balanced without rotating.

The two basic principles of stability are given below:

1. **Lowering the Center of Gravity:** Placing heavier objects at a lower point within a system lowers the center of gravity, enhancing stability.

2. **Widening the Base:** Increasing the base area provides better support and reduces the chances of tipping over, thereby improving stability.

**Examples:**
• **Racing Cars:** To enhance the stability of racing cars, their centers of mass are kept as low as possible. Their base areas are also increased by keeping the wheels outside of their main bodies.

• **Balancing Toys:** These toys have a low center of gravity to ensure they return to their upright position when tilted. This makes them stable and resistant to falling over.

Centripetal force always acts perpendicular to the velocity in uniform circular motion because the velocity is tangent to the circle, while the centripetal force is directed toward the center. This force changes the direction of the velocity, keeping the object in circular motion, without altering its speed. Therefore, centripetal force is perpendicular to the velocity vector at all times.

The moment of force is applicable in the working of a bottle opener. A small force applied at a longer moment arm produces more torque, making it easier to open a bottle.

Smaller diameter steering wheels are used because they allow for quicker and easier turning of the wheel. With power steering less force is needed and a smaller diameter reduces the amount of rotation required to turn the wheels making steering more responsive and effortless.

A tight rope walker balances himself by holding a bamboo stick which helps distribute his weight evenly and lowers his center of gravity. This is done by applying the principle of moments to maintain stability.

As we know, lower the centre of gravity, greater will be stability. In order to lower the center of gravity, acrobats hold a long rod in their hands so that the acrobats may remain in stable equilibrium.

Trigonometry is a branch of mathematics that deals with the properties of a right-angled triangle. The trigonometric ratios are the relationships between the sides of a right-angled triangle.

• Sine θ = Perpendicular/Hypotenuse
• Cosine θ = Base/Hypotenuse
• Tangent θ = Perpendicular/Base

The stability of a racing car is enhanced by keeping its center of mass as low as possible and increasing its base area by positioning the wheels outside of its main body.

From the relation of torque: τ = r × F → τ ∝ r

When force is constant, the torque is directly proportional to moment arm. So, greater the moment arm, greater will be the torque and vice versa. That’s why door knobs (handles) are fixed at the edge of door to increase the moment arm. In this way even a small force is sufficient to produce the required torque, which helps in the opening or closing of the door.

If the door knob is at the middle of the door, the moment arm will become half and you will need a double force to open/close the door as compared to the edge knob.

We know that, τ = rF sinθ

When a satellite of mass “m” is moving around the earth in a circular orbit of radius “r”, then the gravitational force is acting toward the centre of earth, so “Fg” is antiparallel to moment arm “r”, so we put θ = 180° in equation we get:

τ = rF sin 180° = rF × 0 ⇒ τ = 0

Thus the gravitational force acting on a satellite does not exert any torque on it.

For complete equilibrium, the following two conditions must be satisfied i.e.
(i) ΣF = 0 and (ii) Στ = 0

Now if ΣF = 0 and Στ ≠ 0, then the body will rotate and will not be in state of complete equilibrium. We can have situations in which an object is not in equilibrium, even though the net force on it is zero.

**Example (i):** When a steering wheel of a car is rotated with two equal and opposite forces, then it will not be in state of equilibrium. Here the net force is zero but the net torque is not zero and hence the wheel is not in state of equilibrium.

**Example (ii):** When the pedals of a bicycle are rotated, the net force is equal to zero but net torque exists in the system. Therefore, due to net torque, the system is not in state of equilibrium.