1. Rotational Dynamics and Static Equilibrium (Cont.)
Chapter 11
Rotational Dynamics and Static Equilibrium (Cont.)
Dr. Jie Zou PHY 1151G Department of Physics

2. Dr. Jie Zou PHY 1151G Department of Physics
Outline
Dynamic Applications of Torque
Applications of Newton’s 2nd law to rotations
Angular Momentum
Conservation of Angular Momentum
Dr. Jie Zou PHY 1151G Department of Physics

3. Dynamic applications of torque
Application of Newton’s second law for rotational motion:
net = I
net : the net torque (or the total torque, );
I: the moment of inertia;
: the angular acceleration
Dr. Jie Zou PHY 1151G Department of Physics

4. Dr. Jie Zou PHY 1151G Department of Physics
Example 1
Consider a disk-shaped pulley of radius R and mass M with a string wrapped around its circumference. Hanging from the string is a mass m. When the mass is released, it accelerates downward and the pulley begins to rotate. If the pulley rotates without friction, the string unwraps without slipping, and the pulley has a moment of inertia of I, what is the acceleration of the mass and the tension in the string?
Dr. Jie Zou PHY 1151G Department of Physics

5. Dr. Jie Zou PHY 1151G Department of Physics
Example 2
A 0.31-kg cart on a horizontal air track is attached to a string. The string passes over a disk-shaped pulley of mass kg and radius m and is pulled vertically downward with a constant force of 1.1 N. Find (a) the tension in the string between the pulley and the cart, and (b) the acceleration of the cart. Answers: (a) 0.97 N; (b) 3.1 m/s2
Note: when the moment of inertia of the pulley cannot be neglected, T1 ≠ T2.
Dr. Jie Zou PHY 1151G Department of Physics

6. Dr. Jie Zou PHY 1151G Department of Physics
Angular Momentum
Definition of angular momentum, L = I.
SI unit: kg·m2/s.
Exercise: Find the angular momentum of a 0.1-kg Frisbee (considered to be a uniform disk of radius 7.5 cm) spinning with an angular speed of 1.15 rad/s.
Dr. Jie Zou PHY 1151G Department of Physics

7. Conservation of angular momentum
If the net external torque acting on a system of objects is zero, the angular momentum is conserved: Lf = Li
Dr. Jie Zou PHY 1151G Department of Physics

8. Dr. Jie Zou PHY 1151G Department of Physics
Example
A student sits on a piano stool holding a sizable mass in each hand. Initially, the student holds his arms outstretched and spins about the axis of the stool with an angular speed of 3.72 rad/s. The moment of inertia in this case is 5.33 kg·m2. If the student pulls his arms in to his chest, reducing the moment of inertia to 1.60 kg·m2. What is the student’s angular speed now? Answer: 12.4 rad/s
Dr. Jie Zou PHY 1151G Department of Physics

9. Dr. Jie Zou PHY 1151G Department of Physics
Homework
See online homework on
Hand-written problems:
Ch. 11, p. 369, Problems: #46, 47.
Dr. Jie Zou PHY 1151G Department of Physics