## Lecture 22: Rotational Dynamics

November 16, 2017

• Study: Ex 10.1; Figs 10.5, 10.6, 10.7; Exs 10.3, 10.4, 10.8; Fig 10.22; Ex 10.12
• Ignore: Constant acceleration formulas in Table 10.1; Exs 10.2, 10.5, 10.6, 10.7

### Objectives

• (Continuing objective) Relate the concepts of rotational motion and gravity to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
• Relate angular position θ, angular velocity ω, angular acceleration α, and time t. Relate linear speed to angular speed and distance. Use the no-slip condition to relate linear motion and rotational motion.
• Relate rotational kinetic energy to rotational inertia and angular velocity. Solve conservation of mechanical energy problems involving rotational kinetic energy.
• Calculate torque from the force and the position that the force is applied. Calculate angular momentum for particles from linear momentum and position, and angular momentum for extended objects from moment of inertia and angular velocity.
• Use Newton's 2nd Law for rotational motion to relate net torque to the product of the moment of inertia and angular acceleration or to the rate of change of angular momentum. Also, combine this with $\vec F_\text{net} = m{\vec a}$ for systems with both angular and linear motion.

### Homework

• Friday's Assigned Problems: A40, A42, A66, A89; CH 10: 4, 12, 18a, 23, 39, 55, 57, 61

Answers: CH 10 #4 no; #12 it doesn't go up as high on the frictionless slope (can you explain why?); #18a 12.1 min.

Notes: For CH 10 #23, calculate the torque when the mouse is at the end, not while running outward. For CH 10 #55, just calculate the time; you don't need to calculate the number of revolutions of the station during the firing.

• TUESDAY's Hand-In Problems: A41, A67; CH 10: 22, 52, 62

### Videos of example problems

To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.
• Video Example #1: Calculating torque. This problem handles torque using some ideas from Lecture #14. However, it can be done using ideas from Lecture #13. ans: 80 N-m, clockwise.
Note: the answer provided in the problem, 40 N-m, is incorrect. All of the steps seem correct except for the final answer.
• Video Example #2: Detailed conservation of energy problem that includes both rotation and translation. ans: 97 m/s
• Video Example #3: A detailed Newton's second law for rotations problem, involving the connection between rotational and translational motion. All the algebra is shown in this problem, and it is pretty long. ans: 1776 N

### Pre-Class Entertainment

• Setting Me Up, by Dire Straits
• Santeria, by Sublime
• Secure Yourself, by the Indigo Girls
• Stolen Dance, by Milky Chance
• Safe and Sound, by Capital Cities