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Answer

A vector is represented in two ways

It is represented by bold face letter such as A, d,r and V etc It can also be represented by a letter with an arrow placed above or below letter such as or

It is represented by a straight line with an arrow head The length of line represents magnitude of vector (according to suitable scale) Arrow head represents the direction of vector Representation magnitude of vector

The magnitude of vector is represented by Light face letter such as A d rand v

Modulus of a vector such as

Answer

(Cartesian Co-ordinate System) The set of two or three mutually perpendicular lines intersecting at a point is called rectangular system

The lines are called coordinate axes

One of these line is called x-axis (or horizontal axis) The other is called y-axis (or vertical axis) The line perpendicular to both x and y axes is called z-axis The point of intersection is called origin

If the system consists of two perpendicular lines then it is called two dimensional coordinate system

If the system consist of three perpendicular lines, then it is called three dimensional co-ordinate system

Q. How is the direction of vector represented in: (i) a plane (ii) space?

Direction of a Vector in plane

It is represented by the angle which the vector makes with Positive x-axis

In anti-clock wise direction

Direction of a vector in Space

It is represented by three angles which the vector makes with x. y and z axes

Answer

It is a graphical method to add of two or more vectors

(i) Resultant vector

(ii) Vector subtraction

(ii) Multiplication of vector by scalar

(iv) Unit vector

(v) Null vector

(vi) Equal vectors

A vector which has the same effect as the combined effect of all the vectors to be added is called resultant vector

The subtraction of a vector is equivalent to the addition of same vector with its direction reversed

A vector can be multiplied by

A vector whose magnitude is equal to one with no units in a given direction is called unit vector is represented by a letter with a cap or hat on it

vector A vector whose magnitude is zero and direction arbitrary is called a null vector It si represented by

The vectors are said to be equal vectors if they have same magnitude

same direction

(regardless of the position of their initial points)

The effective value of a vector in a given direction is called component of a vector A vector may split up into two or more than two parts these parts are known as components of vector Rectangular Components of Vector

The components of a vector which are perpendicular to each other are called rectangular components

Answer

The turning effect of force produced in a body about an axis is called torque.

The product of magnitude force and the perpendicular distance from axis of rotation to line of action of force is called torque.

The moment of a force can also be defined as the vector product of the radius vector from the axis of rotation to the point of application of the force and the force vector

2. Dynamic equilibrium If a body is moving with uniform velocity. It is said to be in dynamic equilibrium

Example

A car moving with uniform linear velocity

Answer

A body is said to be in equilibrium if it is at rest or moving with uniform velocity under the action a number of forces

There are two types of equilibrium

If a body is at rest It is said to be in static equilibrium Examples

Answer

When first conditions satisfied is linear acceleration of body is zero and the body is said to in translational equilibrium

When second condition is satisfied, angular acceleration of body is zero and the body is said to in rotational equilibrium

Thus for a body to be in complete equilibrium both conditions must be satisfied ie both in ear acceleration and angular acceleration must be zero

1 We will apply the conditions of equilibrium to situations in which all the forces are coplanar

2 To calculate to torque we choose an axis The position of axis is arbitrary

3 A most suitable place is one through which of action of many forces pass

**Q How is vector represented**Answer

**Vector Representation**A vector is represented in two ways

- Symbolic representation
- Graphical representation

**Symbolic Representation**It is represented by bold face letter such as A, d,r and V etc It can also be represented by a letter with an arrow placed above or below letter such as or

**Graphical Representation**It is represented by a straight line with an arrow head The length of line represents magnitude of vector (according to suitable scale) Arrow head represents the direction of vector Representation magnitude of vector

The magnitude of vector is represented by Light face letter such as A d rand v

Modulus of a vector such as

**Q. What is rectangular coordinate system?**Answer

**Rectangular Coordinate System**(Cartesian Co-ordinate System) The set of two or three mutually perpendicular lines intersecting at a point is called rectangular system

The lines are called coordinate axes

One of these line is called x-axis (or horizontal axis) The other is called y-axis (or vertical axis) The line perpendicular to both x and y axes is called z-axis The point of intersection is called origin

**Two dimensional coordinate system (Plane)**If the system consists of two perpendicular lines then it is called two dimensional coordinate system

**Three dimensional co-ordinate system (Space)**If the system consist of three perpendicular lines, then it is called three dimensional co-ordinate system

Q. How is the direction of vector represented in: (i) a plane (ii) space?

**Answer**Direction of a Vector in plane

It is represented by the angle which the vector makes with Positive x-axis

In anti-clock wise direction

Direction of a vector in Space

It is represented by three angles which the vector makes with x. y and z axes

**Q. Describe the addition of vectors by head to tail rule. Is vector addition commutative?**Answer

**Head to Tail Tule**It is a graphical method to add of two or more vectors

**Q. Explain the following terms:**(i) Resultant vector

(ii) Vector subtraction

(ii) Multiplication of vector by scalar

(iv) Unit vector

(v) Null vector

(vi) Equal vectors

**(i) Resultant vector**A vector which has the same effect as the combined effect of all the vectors to be added is called resultant vector

**(ii) Vector subtraction**The subtraction of a vector is equivalent to the addition of same vector with its direction reversed

**(iii) Multiplication of vector by a scalar**A vector can be multiplied by

- A positive number
- A negative number

**(iv) A scalar with dimension Unit vector**A vector whose magnitude is equal to one with no units in a given direction is called unit vector is represented by a letter with a cap or hat on it

**(v) Null or Zero**vector A vector whose magnitude is zero and direction arbitrary is called a null vector It si represented by

**(vi) Equal vectors**The vectors are said to be equal vectors if they have same magnitude

same direction

(regardless of the position of their initial points)

**Q Define component of vector? what are rectangular components of vector**Answer**Component of a vector**The effective value of a vector in a given direction is called component of a vector A vector may split up into two or more than two parts these parts are known as components of vector Rectangular Components of Vector

The components of a vector which are perpendicular to each other are called rectangular components

**Q. Define and explain the term torque of moment of force.**Answer

**Torque****Definition**The turning effect of force produced in a body about an axis is called torque.

**Other Definition**The product of magnitude force and the perpendicular distance from axis of rotation to line of action of force is called torque.

**OR**The moment of a force can also be defined as the vector product of the radius vector from the axis of rotation to the point of application of the force and the force vector

2. Dynamic equilibrium If a body is moving with uniform velocity. It is said to be in dynamic equilibrium

Example

A car moving with uniform linear velocity

**Q.. What is equilibrium? Give its types. What are its different kinds? Also write down the conditions of equilibrium**Answer

**Equilibrium**A body is said to be in equilibrium if it is at rest or moving with uniform velocity under the action a number of forces

**Types of equilibrium**There are two types of equilibrium

**1. Static equilibrium**If a body is at rest It is said to be in static equilibrium Examples

- Book lying on a table
- A body is rotating with uniform angular velocity Motion of a paratrooper

**Q. Under what conditions the body is said to be in complete equilibrium?**Answer

**Translational equilibrium**When first conditions satisfied is linear acceleration of body is zero and the body is said to in translational equilibrium

**Rotational equilibrium**When second condition is satisfied, angular acceleration of body is zero and the body is said to in rotational equilibrium

Thus for a body to be in complete equilibrium both conditions must be satisfied ie both in ear acceleration and angular acceleration must be zero

**Note**1 We will apply the conditions of equilibrium to situations in which all the forces are coplanar

2 To calculate to torque we choose an axis The position of axis is arbitrary

3 A most suitable place is one through which of action of many forces pass

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