physics chapter 2

Question 1

What is the Cartesian coordinate system?

Answer 1

The Cartesian coordinate system uses perpendicular axes to define points in 2D (x, y) or 3D (x, y, z) space, where each axis represents a dimension.

Question 2

How do you add vectors using the head-to-tail rule?

Answer 2

Place the tail of the second vector at the head of the first vector. The resultant is a vector from the tail of the first vector to the head of the second.

Question 3

Define a resultant vector.

Answer 3

A resultant vector is a single vector that represents the combined effect of two or more vectors

Question 4

How do you resolve a vector into rectangular components?

Answer 4

Split the vector into two perpendicular components using the formulas:

Horizontal component: A x =Acosθ
Vertical component: A y=Asinθ

Question 5

What is a unit vector?

Answer 5

A vector with a magnitude of 1, is used to indicate direction.

Question 6

What is the scalar product (dot product) of two vectors?

Answer 6

The scalar product of two vectors is given by A⋅B=ABcosθ, resulting in a scalar quantity.

Question 7

state a property of the scalar product.

Answer 7

A: The scalar product is commutative, meaning A⋅B=B⋅A.

Question 8

What is the vector product (cross product) of two vectors?

Answer 8

The vector product of two vectors is given by A×B=ABsinθn resulting in a vector perpendicular to both A
and B.

Question 9

State a property of the vector product.

Answer 9

The vector product is anti-commutative, meaning A×B=−(B×A).

Question 10

What is equilibrium?

Answer 10

A: Equilibrium occurs when an object experiences no net force or torque, either remaining at rest (static) or moving at constant velocity (dynamic).

Question 11

How is torque related to vector products?

Answer 11

A: Torque is the vector product of the position vector (r) and force (F), given by τ=r×F.

Question 12

What is the second condition of equilibrium?

Answer 12

A: The sum of all torques acting on a body must be zero:
Στ=0.

Question 12

What is the first condition of equilibrium?

Answer 12

A: The sum of all forces acting on a body must be zero:
ΣF=0.

Question 13

Why do you spread your legs on a bumpy bus to maintain balance?

Answer 13

A: Spreading your legs increases your base of support and lowers your center of gravity, helping you maintain equilibrium and prevent falling.

Question 14

What is the difference between a scalar and a vector quantity?

Answer 14

A: A scalar quantity has only magnitude (e.g., mass, temperature), while a vector quantity has both magnitude and direction (e.g., velocity, force).

Question 15

Why is the right-hand rule important in vector products?

Answer 15

A: The right-hand rule helps determine the direction of the resultant vector in a cross product by orienting the thumb of your right hand along the first vector and curling your fingers toward the second vector. The resultant vector points out from your palm.

Question 15

What is a position vector?

Answer 15

A: A position vector points from the origin of a coordinate system to a specific point in space, describing the location of that point relative to the origin.

Question 16

What is the significance of unit vectors in vector notation?

Answer 16

A: Unit vectors (i, j, k ) are used to specify direction along the x, y, and z axes, respectively, in 2D or 3D space. They help express vectors in component form.

Question 17

What is meant by the moment arm in torque calculations?

Answer 17

A: The moment arm is the perpendicular distance from the axis of rotation to the line of action of the force. It plays a key role in determining the magnitude of torque (τ=rFsinθ).

Question 17

What is a balanced force system?

Answer 17

A: A balanced force system occurs when all the forces acting on an object cancel each other out, resulting in no acceleration (the object is either stationary or moving at constant velocity).

Question 18

What is the importance of the angle in vector operations?

Answer 18

A: The angle between two vectors affects both the scalar and vector products:

For the dot product:
A⋅B=ABcosθ, the angle affects the magnitude of the scalar result.

For the cross product:
A×B=ABsinθ, the angle determines the magnitude and direction of the resultant vector.

Question 19

How do non-concurrent forces affect equilibrium?

Answer 19

A: Non-concurrent forces (forces not acting at a single point) can cause rotation in addition to translation. For equilibrium, both the sum of the forces (ΣF=0) and the sum of the torques (Στ=0) must be zero.

Question 20

What is static vs dynamic equilibrium?

Answer 20

A: Static equilibrium occurs when an object is at rest, and all forces/torques are balanced. Dynamic equilibrium occurs when an object is moving at constant velocity, with no net force or torque acting on it.

Question 20

How can you increase torque without increasing force?

Answer 20

A: You can increase torque by increasing the length of the moment arm. For example, using a longer wrench to tighten a bolt increases torque without needing to apply more force.

Question 21

Why are perpendicular vectors easier to add geometrically?

Answer 21

A: When vectors are perpendicular, their components do not influence each other, and the resultant can be easily found using the Pythagorean theorem:
R=(Ax^2 + Ay^2)^1/2

Question 22

What is the principle of moments?

Answer 22

A: The principle of moments states that for rotational equilibrium, the sum of the clockwise moments about any point must equal the sum of the counterclockwise moments:
Στ clockwise = Στ anticlockwise

Question 23

What is a free-body diagram (FBD)?

Answer 23

A: A free-body diagram is a graphical representation that shows all the forces acting on an object. It is a helpful tool for solving equilibrium and force-related problems.

Question 24

What is the relationship between force and acceleration in equilibrium?

Answer 24

A: In equilibrium, the net force acting on an object is zero, meaning there is no acceleration. This is in accordance with Newton’s First Law of Motion (an object at rest stays at rest, or an object in motion stays in motion unless acted upon by an external force).