Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To find the linear speed [tex]\( v \)[/tex] of a point traveling at a constant speed along the circumference of a circle, we use the relationship between linear speed [tex]\( v \)[/tex], radius [tex]\( r \)[/tex], and angular speed [tex]\( \omega \)[/tex]. The formula is given by:
[tex]\[ v = r \times \omega \][/tex]
Given the radius [tex]\( r \)[/tex] of the circle is [tex]\( 35 \)[/tex] inches and the angular speed [tex]\( \omega \)[/tex] is [tex]\( \frac{3\pi}{7} \)[/tex] radians per second, we substitute these values into the formula.
First, substituting the radius:
[tex]\[ r = 35 \text{ inches} \][/tex]
Next, substituting the angular speed:
[tex]\[ \omega = \frac{3\pi}{7} \text{ radians per second} \][/tex]
Now, we calculate the linear speed:
[tex]\[ v = 35 \text{ inches} \times \frac{3\pi}{7} \text{ radians per second} \][/tex]
Perform the multiplication:
[tex]\[ v = 35 \times \frac{3\pi}{7} \][/tex]
Simplify the expression by multiplying:
[tex]\[ v = \frac{35 \times 3\pi}{7} \][/tex]
[tex]\[ v = \frac{105\pi}{7} \][/tex]
Finally, simplify the division:
[tex]\[ v = 15 \pi \text{ inches per second} \][/tex]
Given this, the exact, fully simplified answer for the linear speed [tex]\( v \)[/tex] is:
[tex]\[ v = 15 \pi \text{ inches per second} \][/tex]
[tex]\[ v = r \times \omega \][/tex]
Given the radius [tex]\( r \)[/tex] of the circle is [tex]\( 35 \)[/tex] inches and the angular speed [tex]\( \omega \)[/tex] is [tex]\( \frac{3\pi}{7} \)[/tex] radians per second, we substitute these values into the formula.
First, substituting the radius:
[tex]\[ r = 35 \text{ inches} \][/tex]
Next, substituting the angular speed:
[tex]\[ \omega = \frac{3\pi}{7} \text{ radians per second} \][/tex]
Now, we calculate the linear speed:
[tex]\[ v = 35 \text{ inches} \times \frac{3\pi}{7} \text{ radians per second} \][/tex]
Perform the multiplication:
[tex]\[ v = 35 \times \frac{3\pi}{7} \][/tex]
Simplify the expression by multiplying:
[tex]\[ v = \frac{35 \times 3\pi}{7} \][/tex]
[tex]\[ v = \frac{105\pi}{7} \][/tex]
Finally, simplify the division:
[tex]\[ v = 15 \pi \text{ inches per second} \][/tex]
Given this, the exact, fully simplified answer for the linear speed [tex]\( v \)[/tex] is:
[tex]\[ v = 15 \pi \text{ inches per second} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.