physics chapter 2 Flashcards

1
Q

What is the Cartesian coordinate system?

A

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.

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2
Q

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

A

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.

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3
Q

Define a resultant vector.

A

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

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4
Q

How do you resolve a vector into rectangular components?

A

Split the vector into two perpendicular components using the formulas:

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

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5
Q

What is a unit vector?

A

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

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6
Q

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

A

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

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7
Q

state a property of the scalar product.

A

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

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8
Q

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

A

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

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9
Q

State a property of the vector product.

A

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

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10
Q

What is equilibrium?

A

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

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11
Q

How is torque related to vector products?

A

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

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12
Q

What is the second condition of equilibrium?

A

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

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12
Q

What is the first condition of equilibrium?

A

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

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13
Q

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

A

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

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14
Q

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

A

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

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15
Q

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

A

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.

15
Q

What is a position vector?

A

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.

16
Q

What is the significance of unit vectors in vector notation?

A

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.

17
Q

What is meant by the moment arm in torque calculations?

A

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).

17
Q

What is a balanced force system?

A

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).

18
Q

What is the importance of the angle in vector operations?

A

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.

19
Q

How do non-concurrent forces affect equilibrium?

A

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.

20
Q

What is static vs dynamic equilibrium?

A

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.

20
Q

How can you increase torque without increasing force?

A

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.

21
Q

Why are perpendicular vectors easier to add geometrically?

A

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

22
Q

What is the principle of moments?

A

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

23
Q

What is a free-body diagram (FBD)?

A

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.

24
Q

What is the relationship between force and acceleration in equilibrium?

A

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).

25
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26
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