A truck is moving at a constant speed. The diameter of its tires is 061.0cm. if the angular speed of the tires is 54.0 radys, what is the (linear) speed. of the trick? (Tires are rolling without slipping or sliding). v = ?
A truck is moving at a constant speed. The diameter of its tires is 061.0cm. if the angular speed of the tires is 54.0 radys, what is the (linear) speed. of the trick? (Tires are rolling without slipping or sliding). v = ?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
![**Problem 1**
A truck is moving at a constant speed. The diameter of its tires is 101.0 cm. If the angular speed of the tires is 54.0 rad/s, what is the (linear) speed of the truck? (Tires are rolling without slipping or sliding).
\[ v = ? \]
---
**Solution Explanation:**
To solve for the linear speed \( v \) of the truck, we will use the relationship between linear speed, angular speed, and the radius of the tires:
\[ v = \omega \times r \]
where \( \omega \) is the angular speed and \( r \) is the radius of the tire.
First, convert the diameter of the tire to the radius:
\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{101.0 \, \text{cm}}{2} = 50.5 \, \text{cm} \]
Convert centimeters to meters since standard SI units should be used:
\[ r = 50.5 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 0.505 \, \text{m} \]
Now, apply the angular speed (\( \omega \)):
\[ \omega = 54.0 \, \text{rad/s} \]
Finally, substitute \( \omega \) and \( r \) into the formula:
\[ v = \omega \times r = 54.0 \, \text{rad/s} \times 0.505 \, \text{m} = 27.27 \, \text{m/s} \]
So, the linear speed \( v \) of the truck is:
\[ v = 27.27 \, \text{m/s} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa49c042c-e715-46d7-b1af-568fb3890c2a%2F2cfbedbd-0b13-4f26-9893-374b36d20ab6%2Fatkgqnm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 1**
A truck is moving at a constant speed. The diameter of its tires is 101.0 cm. If the angular speed of the tires is 54.0 rad/s, what is the (linear) speed of the truck? (Tires are rolling without slipping or sliding).
\[ v = ? \]
---
**Solution Explanation:**
To solve for the linear speed \( v \) of the truck, we will use the relationship between linear speed, angular speed, and the radius of the tires:
\[ v = \omega \times r \]
where \( \omega \) is the angular speed and \( r \) is the radius of the tire.
First, convert the diameter of the tire to the radius:
\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{101.0 \, \text{cm}}{2} = 50.5 \, \text{cm} \]
Convert centimeters to meters since standard SI units should be used:
\[ r = 50.5 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 0.505 \, \text{m} \]
Now, apply the angular speed (\( \omega \)):
\[ \omega = 54.0 \, \text{rad/s} \]
Finally, substitute \( \omega \) and \( r \) into the formula:
\[ v = \omega \times r = 54.0 \, \text{rad/s} \times 0.505 \, \text{m} = 27.27 \, \text{m/s} \]
So, the linear speed \( v \) of the truck is:
\[ v = 27.27 \, \text{m/s} \]
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