Physics Vector Components and Units Quiz

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Questions and Answers

What is the formula for calculating the x-component of a vector?

$Ax = A cos \theta$ (correct)

$Ax = A tan \theta$

$Ax = A sin \theta$

$Ax = A + \theta$

Under what condition can the equations for vector components be applied accurately?

If θ is measured with respect to the y-axis

If the vector has equal x and y components

If θ is measured with respect to the x-axis (correct)

If the vector's magnitude is greater than zero

What distinguishes a vector from a scalar?

Scalars can be represented by arrows.

Vectors solely have magnitude.

Vectors contain magnitude and direction. (correct)

Scalars have both magnitude and direction.

What happens to the x-component and y-component of a vector when θ equals 90°?

$Ax = 0; Ay = A$ Signup and view all the answers

Which of the following is a scalar quantity?

Speed Signup and view all the answers

If $Ax$ is negative, which of the following can be inferred about the angle θ?

θ is between 90° and 180° Signup and view all the answers

What is required to properly define a vector quantity?

Magnitude and direction. Signup and view all the answers

What is the relationship between the components of a vector and its magnitude?

$A = Ax + Ay$ Signup and view all the answers

How is the magnitude of a vector denoted?

With absolute value signs. Signup and view all the answers

Which of the following statements is true about vector quantities?

They are more complex than scalar quantities. Signup and view all the answers

What happens to the order of magnitude if the multiplier in scientific notation is greater than 3.162?

It increases by one compared to the power of 10. Signup and view all the answers

In estimating the number of breaths taken during a lifetime, why is 10 breaths per minute a better estimate than 1 or 100?

It takes into account variations in activity levels. Signup and view all the answers

Which of the following is NOT considered a significant figure?

The digit in the number 200. Signup and view all the answers

Why is it important to consider uncertainty in measurements?

It impacts the reliability of the results in calculations. Signup and view all the answers

Which of the following statements about significant figures is true?

Leading zeros in decimal numbers are not significant. Signup and view all the answers

Which of the following statements about dimensional analysis is true?

Quantities can be added or subtracted as long as they are in the same units. Signup and view all the answers

In the equation s = a + b, what are the dimensions of s if a and b have units of meters?

meters Signup and view all the answers

How would you convert a speed limit of 100 km/h to miles per hour?

Multiply by 0.621 Signup and view all the answers

If a car is traveling at 38.0 m/s, what is its speed in kilometers per hour?

136.8 km/h Signup and view all the answers

Which prefix corresponds to 10 raised to the power of 6?

mega Signup and view all the answers

What is the correct order of magnitude for the mean radius of the Earth, approximately 6,371 km?

10^6 km Signup and view all the answers

If the conversion from miles to kilometers uses 1 mile = 1.609 km, what is the equivalent of 200 miles in kilometers?

321.8 km Signup and view all the answers

Which of the following is an example of a unit that can cancel in dimensional analysis?

meters in distance and centimeters in distance Signup and view all the answers

When adding two vectors graphically, where is the resultant vector drawn?

From the origin of the first vector to the end of the last vector Signup and view all the answers

What does vector subtraction involve?

Adding the negative of the subtracted vector to the original vector Signup and view all the answers

Which of the following describes a vector?

Described by number, units, direction, and magnitude Signup and view all the answers

In the polygon method for adding vectors, what should be done after drawing the first vector?

Draw the next vector from the tip of the first vector Signup and view all the answers

What is necessary to accurately describe a vector algebraically?

Magnitude and direction are essential Signup and view all the answers

Study Notes

Components of a Vector

A component is a part of a vector.
Rectangular components are the projections of a vector along the x and y-axes.
The x-component of a vector is the projection along the x-axis.
The y-component of a vector is the projection along the y-axis.
The components can be positive or negative and will have the same units as the original vector.

Dimensional Analysis

Necessary to either derive a math expression or equation or to check its correctness.
Quantities can be added/subtracted only if they have the same dimensions.
The terms of both sides of an equation must have the same dimensions.

Conversion of Units

Units can be treated like algebraic quantities that can cancel each other out.

Prefixes

Prefixes correspond to powers of 10.
Each prefix has a specific name and abbreviation.

Estimates and Order-of-Magnitude Calculations

Order of magnitude is a power of ten determined by expressing the number in scientific notation.
If the multiplier is less than 3.162, the order of magnitude of the number is the power of 10 in the scientific notation.
If the multiplier is greater than 3.162, the order of magnitude is one larger than the power of 10 in the scientific notation.

Uncertainty in Measurements

There is uncertainty in every measurement.
This uncertainty carries over through calculations.
Significant figures are used to approximate the uncertainty in results of calculations.

Significant Figures

A significant figure is one that is reliably known.
It is the number of numerical digits used to express the measurement.
All non-zero digits are significant.
Zeros are significant when they are between other non-zero digits, after the decimal point and another significant figure, or can be clarified by using scientific notation.

Vector and Scalar Quantities

A vector quantity has both magnitude and direction.
A scalar is completely specified by only a magnitude.
Vectors can be described by their magnitude and direction and by their components.

Adding Vectors Graphically

When adding multiple vectors, the resultant is drawn from the origin of the first vector to the end of the last vector.

Adding Vectors Geometrically (Polygon Method)

Draw the first vector with the appropriate length and direction.
Draw the next vector with the appropriate length and direction, starting at the end of the first vector.
Continue drawing vectors, starting at the end of the previous vector.
The resultant is drawn from the origin of the first vector to the end of the last vector.

Vector Subtraction

Vector subtraction is a special case of vector addition involving the negative of the subtracted vector.
Continue with standard vector addition procedure.

Describing Vectors Algebraically

Vectors can be described by their magnitude, units, and direction.
Vectors can be described by their components.

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Description

Test your knowledge on vector components, dimensional analysis, unit conversions, and order-of-magnitude calculations. This quiz covers essential concepts in physics that are fundamental to understanding how to manipulate and interpret physical quantities.