Transcript Circular Motion

Circular Motion: Problem
Solving
8.01
W04D3
Today’s Reading Assignment:
W04D3
Problem Solving Strategy: Circular Motion
Dynamics
Concept Question: Tension
and String Theory
A ball is suspended from a
vertical rod by two strings
of equal strength and equal
length. The strings are very
light and do not stretch.
The rod is spun with a
constant angular
acceleration. Which string
breaks first?
1.
2.
3.
4.
the upper string
the lower string
they break simultaneously
cannot tell without more
information
Group Problem: Tension
and String Theory
A ball of mass m is
suspended from a vertical
rod by two strings of equal
strength and equal length l.
The strings are very light
and do not stretch. The rod
is spun with a constant
angular speed ω. What are
the tensions in the two
strings?
Group Problem: Tension in
Strings
Two objects of equal mass m are whirling around a shaft with
a constant angular velocity ω. The first object is a distance d
from the central axis, and the second object is a distance 2d
from the axis. You may ignore the mass of the strings and
neglect the effect of gravity. What are tensions in the string
between the inner object and the outer object and the string
between the shaft and the inner object?
Group Problem: Tension in a
Spinning Rope
A uniform rope of mass m and length L
is attached to shaft that is
rotating at constant angular velocity ω.
You may ignore the effect of gravitation.
a) Divide the rope into small pieces of length Δr. Consider the piece located a
distance r from the shaft. Draw a free body force diagram on that small piece.
b) Apply Newton’s Second Law to that small piece and find in the limit as Δr
approaches zero, a differential equation relating dT/dr to the distance r from the
shaft.
c) Integrate the differential equation you found in part b) to find the tension in
the rope as a function of distance from the shaft.
Next Reading Assignment:
W05D1
Young and Freedman: 6.1-6.4
Review Module: Scalar Product