Physics 141, Fall 2023.

1.     (50%) WeBWorK set # 8.

 

2.     (25%) A string is wrapped around an object of mass M, radius R, and moment of inertia I.  A constant force F is applied to one end of the string, as indicated in the Figure below.  We observe that the object does not move up or down, but it increases its angular velocity.

 

a.     What is the angular acceleration of the object?

b.     When you have moved the end of the string to a height y₀ above the floor, the object is rotating with an angular velocity w₀.  What is the angular velocity w of the object when you have moved the end of the string to a height y above the floor?

 

3.     (25%) A uniform stick of mass M and length L is lying on ice.  A small mass m, traveling at high speed v_i, strikes the stick a distance d from its center.  The mass m bounces of the stick with speed v_f, as shown in the Figure.  The angles between the initial and the final velocities with respect to the x axis are q_i and q_f.

a.     What are the x and y components of the velocity of the center of the stick after the collision?

b.     What are the magnitude and the direction of the angular velocity of the stick after the collision?

c.     What is the increase in the thermal energy of the objects?

 

4.     (Optional; 25% extra credit) You can download the barbell_ang_mom.py program from our web site.  This program is simulates the motion of a barbell attached to the end of a rotating rod.  Modify the code to obtain information about the angular momenta of the blue and red balls that make up the barbell, and about the total angular momentum of the barbell.  Use this information to make graphs of the angular momenta as function of time.  By clicking in the window you can switch modes (the orientation of the barbell is fixed, the orientation of the barbell changes at the same rate as the rotating rod, or the orientation of the barbell changes at a rate much higher than the rotation rate of the rod).  Send these graphs and the actual program (after you modified it to generate the output you need) via email to Professor Wolfs (wolfs@pas.rochester.edu).  The name of the file with the program should be hw08p04XXYYYYYYYY.py where XX are your initials and YYYYYYYY is your student id number.