Problem Solving TwoDimensional Rotational Dynamics 8 01 W

Problem Solving Two-Dimensional Rotational Dynamics 8. 01 W 09 D 3

Today’s Reading Assignment: W 09 D 3 Young and Freedman: 1. 10 (Vector Product) 10. 1 -10. 2, 10. 5 -10. 6 ; 11. 111. 3

Table Problem: Person on Ladder A person of mass mp is standing on a rung, one third of the way up a ladder of length d. The mass of the ladder is ml and is uniformly distributed. The ladder is initially inclined at an angle θ with respect to the horizontal. Assume that there is no friction between the ladder and the wall but that there is friction between the base of the ladder and the floor with a coefficient of static friction μs. In this problem you will try to find the minimum coefficient of friction μs between the ladder and the floor so that the person and ladder do not slip.

Table Problem: Atwood’s Machine A pulley of mass mp, radius R, and moment of inertia Icm about the center of mass, is suspended from a ceiling. An inextensible string of negligible mass is wrapped around the pulley and attached on one end to an object of mass m 1 and on the other end to an object of mass m 2 , with m 1 > m 2. At time t = 0, the objects are released from rest. Find the magnitude of the acceleration of the objects.

Analysis: Atwood’s Machine Free body force diagrams and force equations:

Analysis: Atwood’s Machine Rotational motion equation: Force equations: Constraint condition: Acceleration: Time to travel distance d:

Next Reading Assignment: W 09 D 3 Young and Freedman: 10. 5 -10. 6