A fishing rod has a mass of O.8 kg. If a fisherman uses 0.8 Nm of torque to give it an angular acceleration of 5 rad/s2, find the length of the fishing rod. Use I = 1/3 m12 for the moment of inertia.
A fishing rod has a mass of O.8 kg. If a fisherman uses 0.8 Nm of torque to give it an angular acceleration of 5 rad/s2, find the length of the fishing rod. Use I = 1/3 m12 for the moment of inertia.
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)...
Related questions
Concept explainers
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
Question
9
![**Problem: Determining the Length of a Fishing Rod**
A fishing rod has a mass of 0.8 kg. If a fisherman uses 0.8 Nm of torque to give it an angular acceleration of 5 rad/s², find the length of the fishing rod. Use the formula for the moment of inertia: \( I = \frac{1}{3} m l^2 \).
**Solution:**
1. **Identify the given values:**
- Mass (\( m \)) = 0.8 kg
- Torque (\( \tau \)) = 0.8 Nm
- Angular acceleration (\( \alpha \)) = 5 rad/s²
2. **Formula for torque related to angular acceleration:**
\[
\tau = I \alpha
\]
Where \( I \) is the moment of inertia of the rod.
3. **Substitute the formula for the moment of inertia:**
\[
I = \frac{1}{3} m l^2
\]
4. **Substitute known values into the torque formula:**
\[
0.8 = \left(\frac{1}{3} \times 0.8 \times l^2\right) \times 5
\]
5. **Solve for \( l \):**
\[
0.8 = \frac{4}{3} l^2
\]
\[
l^2 = \frac{0.8 \times 3}{4}
\]
\[
l^2 = 0.6
\]
\[
l = \sqrt{0.6}
\]
\[
l \approx 0.775 \, \text{m}
\]
Therefore, the length of the fishing rod is approximately 0.775 meters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1d700aa-072a-4ff7-be1d-cdca0f10aa9d%2Fbb22677f-42b8-486d-b4af-665f079581ee%2Fs72upc6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Determining the Length of a Fishing Rod**
A fishing rod has a mass of 0.8 kg. If a fisherman uses 0.8 Nm of torque to give it an angular acceleration of 5 rad/s², find the length of the fishing rod. Use the formula for the moment of inertia: \( I = \frac{1}{3} m l^2 \).
**Solution:**
1. **Identify the given values:**
- Mass (\( m \)) = 0.8 kg
- Torque (\( \tau \)) = 0.8 Nm
- Angular acceleration (\( \alpha \)) = 5 rad/s²
2. **Formula for torque related to angular acceleration:**
\[
\tau = I \alpha
\]
Where \( I \) is the moment of inertia of the rod.
3. **Substitute the formula for the moment of inertia:**
\[
I = \frac{1}{3} m l^2
\]
4. **Substitute known values into the torque formula:**
\[
0.8 = \left(\frac{1}{3} \times 0.8 \times l^2\right) \times 5
\]
5. **Solve for \( l \):**
\[
0.8 = \frac{4}{3} l^2
\]
\[
l^2 = \frac{0.8 \times 3}{4}
\]
\[
l^2 = 0.6
\]
\[
l = \sqrt{0.6}
\]
\[
l \approx 0.775 \, \text{m}
\]
Therefore, the length of the fishing rod is approximately 0.775 meters.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON