Snapsolve any problem by taking a picture. Try it in the Numerade app?
Question
Suppose a point moves along a circle with radius $r$ as shown in the figure below. The point travels a distance $s$ along the circle in time $t$(a) The angular speed of the point is $\omega=$___.(b) The linear speed of the point is $v=$___.(c) The linear speed $v$ and the angular speed $\omega$ are related bythe equation $v=$___.(FIGURE CANNOT COPY)
Instant Answer
Step 1
In this case, the point is moving through an angle $\theta$ in time $t$. Therefore, the angular speed $\omega$ is given by the ratio of the angle to the time. Mathematically, this is represented as: \[\omega = \frac{\theta}{t}\] Show more…
Show all steps
Linda Hand and 100 other Precalculus educators are ready to help you.
Ask a new question
Recommended Videos
An object travels around a circle of radius $r$ with constant speed. If $s$ is the distance traveled in time $t$ around the circle and $\theta$ is the central angle (in radians) swept out in time $t,$ then the linear speed of the object is $v=$ ________ and the angular speed of the object is $\omega=$ _____.
Suppose that point $P$ is on a circle with radius $r$, and ray $O P$ is rotating with angular speed $\omega .$ Use the given values of $r, \omega,$ and $t$ to do the following. See Example $5 .$ (a) Find the angle generated by $P$ in time $t$. (b) Find the distance traveled by $P$ along the circle in time $t$. (c) Find the linear speed of $P$. $r=30 \mathrm{~cm}, \omega=\frac{\pi}{10}$ radian per sec, $t=4 \mathrm{sec}$
The Circular Functions and Their Graphs
The Unit Circle and Circular Functions
If $v$ is the ___________ velocity of a point on a circle of radius $r$ and $\omega$ is its _________ velocity, then $v=r \omega$
The Trigonometric Functions
Angles and Their Measurements
Transcript
Watch the video solution with this free unlock.
Not finding what your looking for? Here are some other ways we can help!
Generate practice questions
Explain a concept
Create a study plan
EMAIL
PASSWORD