ENGR2302 Rotational motion Lab Name: _________________
1.
(15.75) A
Frisbee moves horizontally in the x direction with a speed of 10 m/s and
has an acceleration of -2 m/s^2 (it’s slowing down).
Knowing that it has a clockwise rotation when viewed from above with an
angular velocity of 100 rad/sec, determine the instantaneous axis of rotation,
and the velocity and accelerations of the points in the figure below. A: x = r,
B: z = +r, C: z = -r.
Concept
quiz: Skim through these notes:
a)
Throw a Frisbee right-side-up and
up-side-down. Which works better? Why? Is it possible to design a Frisbee that
has even more lift? Draw a new Frisbee design;
include arrows showing the velocity profile.
b)
Try to give the Frisbee a forward velocity
without spinning it. Now try tossing it
with a very slow rotation, and then a fast rotation. Why does an increased angular momentum (mrv)
stabilize the motion? ( Angular momentum is a body’s resistance to change in
its orientation and rate of rotation, just like linear moment is a body’s
resistance to change in it’s velocity. –
Inertia!)
Try out the bike
wheel + spinning chair. The spinning
wheel does not want to be re-oriented, it’s stable when it is spinning!
2.
Yo-Yo
physics!
a)
Potential energy → kinetic energy.
If the yo-yo starts at a height of 5 ft, and is allowed to unwind until
it reaches the ground, what is it’s linear and rotational velocity just before
it hits the ground? (measure the
diameter of your yo-yo’s axis)
b)
What is the angular
momentum of the yo-yo at the end of its string?
Why does the yo-yo want to climb back up its string? (think back to the Frisbee problem, and think
about angular momentum again)
Why is the yo-yo’s axis
perpendicular to its string when it is rotating?
c)
Why is a
little tug needed in order to keep the yo-yo moving?
d)
Explain
the angular accelerations and velocities at play for your favorite yo-yo trick
(walk the dog? Sleep?)
3.
Slinky
As a slinky goes down the stairs, what is
the velocity of a point on its outer edge, as opposed to its velocity on its
inner edge? Where is the instantaneous
center of rotation?
4. Spirograph
Choose a circle and a track out of the Spirograph
kit, and sketch out a pattern. If the
circle has a constant angular velocity about its center, how does the velocity
of where your pencil tip is vary? Label
your Spirograph art with the velocity of your pencil tip if the art was created
using constant angular velocity of the circle.
Where was the velocity max? Where
was it a minimum? Why?
Draw a new sketch – this time
label the accelerations of where your pencil tip was, again assuming that the
circle had a constant angular velocity through the entire process. Where do max and min accelerations happen?
5. Water
Wheel assembly:
If a river imparts a tangential velocity of 10 m/s to the
end of the clear water-wheel paddle, what are the angular velocities of all of
the gears?
6. Gears with rods:
Solve for the maximum horizontal velocity
of the end of the lower rod dragging along the ground as a function of the
angular velocity of the gear at the top of the assembly.
Solve for the maximum angular velocity and
acceleration of the lower rod as a function of the angular velocity of the gear at the top of the assembly.
