7.5. It's a rough approximation, but let's treat a spinning ice skater as a solid cylinder with a radius of 0.25 m. (a) If their mass is 55 kg, what is their rotational inertia? (b) Calculate the magnitude of the angular momentum of a 55 kg ice skater spinning 6 times a second. (c) Calculate the total kinetic energy of this skater if they are spinning at a rate of 6 rotations per second while traveling through the air at a rate of 2 m/s.
7.5. It's a rough approximation, but let's treat a spinning ice skater as a solid cylinder with a radius of 0.25 m. (a) If their mass is 55 kg, what is their rotational inertia? (b) Calculate the magnitude of the angular momentum of a 55 kg ice skater spinning 6 times a second. (c) Calculate the total kinetic energy of this skater if they are spinning at a rate of 6 rotations per second while traveling through the air at a rate of 2 m/s.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
I need help on question 7.5?
![## 7.4 Vector Cross Product
**Given:**
\[
\vec{A} =
\begin{bmatrix}
4.0 \, \text{m} \\
-2.0 \, \text{m}
\end{bmatrix}
\quad \text{and} \quad
\vec{B} =
\begin{bmatrix}
-2.0 \, \text{N} \\
5.0 \, \text{N}
\end{bmatrix}
\]
**(a)** Draw a diagram with both vectors starting at the origin and express both vectors as magnitude and direction. What is the angle between the two vectors?
**(b)** Show that \(\vec{A} \times \vec{B} = 16 \, \text{Nm} \, \hat{z}\) by using the formula \(|\vec{A}||\vec{B}|\sin\theta\) and the right-hand rule.
**(c)** Find \(\vec{A} \times \vec{B}\) by using matrix multiplication: \((A_xB_y - A_yB_x)\hat{z}\).
---
## 7.5 Rotational Dynamics of an Ice Skater
It’s a rough approximation, but let’s treat a spinning ice skater as a solid cylinder with a radius of 0.25 m.
**(a)** If their mass is 55 kg, what is their rotational inertia?
**(b)** Calculate the magnitude of the angular momentum of a 55 kg ice skater spinning 6 times a second.
**(c)** Calculate the total kinetic energy of this skater if they are spinning at a rate of 6 rotations per second while traveling through the air at a rate of 2 m/s.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F528139fc-f068-48e7-ab76-1df2a6cdbb70%2F19758abe-4aa0-4de7-a614-6a9232cbe8d8%2F2h3oym6e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## 7.4 Vector Cross Product
**Given:**
\[
\vec{A} =
\begin{bmatrix}
4.0 \, \text{m} \\
-2.0 \, \text{m}
\end{bmatrix}
\quad \text{and} \quad
\vec{B} =
\begin{bmatrix}
-2.0 \, \text{N} \\
5.0 \, \text{N}
\end{bmatrix}
\]
**(a)** Draw a diagram with both vectors starting at the origin and express both vectors as magnitude and direction. What is the angle between the two vectors?
**(b)** Show that \(\vec{A} \times \vec{B} = 16 \, \text{Nm} \, \hat{z}\) by using the formula \(|\vec{A}||\vec{B}|\sin\theta\) and the right-hand rule.
**(c)** Find \(\vec{A} \times \vec{B}\) by using matrix multiplication: \((A_xB_y - A_yB_x)\hat{z}\).
---
## 7.5 Rotational Dynamics of an Ice Skater
It’s a rough approximation, but let’s treat a spinning ice skater as a solid cylinder with a radius of 0.25 m.
**(a)** If their mass is 55 kg, what is their rotational inertia?
**(b)** Calculate the magnitude of the angular momentum of a 55 kg ice skater spinning 6 times a second.
**(c)** Calculate the total kinetic energy of this skater if they are spinning at a rate of 6 rotations per second while traveling through the air at a rate of 2 m/s.
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 3 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
