Textbook Question
Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―8π/5
Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 4, Problem 36
Find the angular speed ω for each of the following.
a gear revolving 300 times per min
Verified step by step guidance1
Understand that angular speed \( \omega \) is the rate of change of angular displacement and is usually measured in radians per second (rad/s).
Given the gear revolves 300 times per minute, recognize that each revolution corresponds to an angular displacement of \( 2\pi \) radians.
Convert the number of revolutions per minute (rpm) to radians per minute by multiplying the revolutions by \( 2\pi \): \( 300 \times 2\pi \) radians per minute.
Convert the angular speed from radians per minute to radians per second by dividing by 60 (since there are 60 seconds in a minute): \( \frac{300 \times 2\pi}{60} \) radians per second.
Simplify the expression to get the angular speed \( \omega \) in radians per second.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Speed (ω)
Angular speed measures how fast an object rotates or revolves, expressed in radians per second. It represents the angle covered per unit time and is a fundamental quantity in rotational motion.
Conversion from Revolutions per Minute to Radians per Second
To find angular speed in radians per second from revolutions per minute (rpm), multiply the rpm by 2π (radians per revolution) and divide by 60 (seconds per minute). This converts the rotational speed into standard angular units.
Recommended video:
03:48
Introduction to Vectors
Relationship Between Linear and Angular Quantities
Understanding how angular speed relates to linear speed and frequency helps in interpreting rotational motion problems. Here, frequency in revolutions per minute is converted to angular speed, linking rotational frequency to angular displacement.
Recommended video:
6:00Categorizing Linear Equations
Related Practice
Textbook Question
Find a calculator approximation to four decimal places for each circular function value. See Example 3. cos (-1.1519)
Textbook Question
Find a calculator approximation to four decimal places for each circular function value. See Example 3. sin 0.6109
Textbook Question
Find a calculator approximation to four decimal places for each circular function value. See Example 3. tan 4.0203
Textbook Question
Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―π/6
3
views
Textbook Question
Find each exact function value.
sin ( ―5π/6)