lab 7; Mar 19 — rotational motion

Lab #7
Physics 111
I. Constant angular velocity
Rotational Motion
Name:
Consider a wheel spinning counter-clockwise at a constant rate
about a fixed axis. The diagram at right represents a snapshot
of the wheel at one instant in time.
A. [3 pts] Draw arrows on the diagram to represent the
magnitude and direction of the tangential velocity, v T
for each of the points A, B, and C at the instant shown.
C
A
B
[3 pts] Rank the magnitudes of the tangential velocities v T of points A, B, and C.
B. Suppose the wheel makes one complete revolution in 2 seconds.
[3 pts] On the diagram at the right, draw the three radius
vectors r A , r B , r C from the pivot point to each point A, B, C.
A
[3 pts] Find the change in angle Δθ made in one second by
the position vector for:
point A
point B
point C
[3 pts] Calculate the angular speed ω=Δθ/Δt of the wheel.
C
B
C. Does the description of a wheel’s rotation depend on your location relative to the wheel
if you specify:
[2 pts] “clockwise” or “counter-clockwise”? yes no (circle one)
[2 pts] the vector ω? yes no (circle one)
[5 pts] Use the wheel provided to have various members of your lab group
demonstrate to a staff member the motion of an object whose angular velocity vector
points
west, parallel (horizontal) to the floor
north, at an angle of 45 0 above horizontal
straight towards your own left shoulder
various other directions for ω as called upon by a staff member…
Rotational Motion–1

Lab #7
Rotational Motion
Physics 111
Name:
II. Changing angular velocity: Be sure to use your wheels for each situation described below.
A. Make the initial angular velocity of a wheel ω 0
point due north, parallel to the lab floor. In
each case described below, determine the magnitude and direction of the change in angular
velocity, which is the vector Δω. Note the compass directions drawn to the right.
North
[3 pts] the wheel were made to
spin faster, keeping the axis of
rotation fixed. Draw this on the
diagram at the right.
ω 0
[3 pts] the wheel were rotated by
90° such that the final angular
velocity is due east, but continued
to spin at the same rate.
ω 0
B. For an object rotating about a fixed axis, describe the relative orientation of ω and α if the
object is:
[3 pts] spinning faster and faster
[3 pts] spinning slower and slower
C. Two geared wheels roll on each other without slipping. One
has twice the radius of the other.
A string is wrapped around the axis of the small wheel
as shown in the diagram, and a 1.0-kg mass is
attached to the string.
radius = 2R
Initially, the larger wheel is held in place such that the entire
apparatus is stationary.
i. The wheels are released so they are free to move.
[3 pts] Is the 1.0-kg mass accelerating? yes no (circle one)
radius = R
[3 pts] Explain how the acceleration compares to that of a freely
falling object (i.e., is the acceleration of the mass 9.8 m/s 2 ?).
Rotational Motion–2

Lab #7
Rotational Motion
Physics 111
ii. During the time that the mass is falling, find:
Name:
[4 pts] the direction of ω for the small wheel. Explain how you determined this
direction.
[4 pts] the direction of α for the small wheel. Explain how you determined this
direction.
iii. During the time that the mass is falling, compare:
[4 pts] the angular velocities (both magnitude and direction) of the large and small
wheels. If one has a larger angular velocity, give a specific number of times larger.
[4 pts] the angular accelerations (both magnitude and direction) of the large and small
wheels. If one has a larger angular acceleration, state how much larger. Explain.
III.
Applications: A bicycle wheel is mounted on a fixed, frictionless axle. A light string is
wound around the wheel’s rim; a weight is attached to the string.
At t = t o , the weight is released from rest; the weight has not started to move.
At t = t 1 , the weight is falling, but the string is still partially wound around the wheel.
At t = t 2 , the weight and string have both reached the ground; the wheel is still turning.
A
A
weight just
released from
rest
weight
falling
A
weight and string
on ground;
wheel still turning
t = t 0 t = t 1 t = t 2
Rotational Motion–3

Lab #7
Physics 111
Rotational Motion
Name:
A. [4 pts] What is the direction of the angular velocity ω of the wheel at each of the three times
shown? If ω=0 at any time, state that explicitly.
B. [4 pts] What is the direction of the wheel’s angular acceleration α at each of the three times
shown? If α=0 at any time, state that explicitly, and explain why you think α = 0.
C. [4 pts] Rank the centripetal acceleration of point A at the three times shown (a c,0 , a c,1 , a c,2 )
from largest to smallest. If any of these is zero, state that explicitly. Explain how you
determined your ranking.
D. Describe a real-life situation involving a turning disk such that each of the following cases is
true. All of the cases below are possible.
[3 pts] α = 0 and a c = 0
[3 pts] α ≠ 0 and a c = 0
[3 pts] α = 0 and a c ≠ 0
[3 pts] α ≠ 0 and a c ≠ 0
Rotational Motion–4