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Homework answers / question archive / University of Texas  PHY 303K Overton, Mays – Midterm 3 1)Two objects, of masses 25 kg and 10 kg, are hung from the ends of a stick that is 70 cm long and has marks every 10 cm, as shown
University of Texas  PHY 303K
Overton, Mays – Midterm 3
1)Two objects, of masses 25 kg and 10 kg, are hung from the ends of a stick that is 70 cm
long and has marks every 10 cm, as shown.
ABCDEF G

















10 
20 
30 
40 
50 
60 

25 kg 
10 kg 
2. A 3 kg bicycle wheel rotating at a 2368 rev/min angular velocity has its shaft supported on one side, as shown in the figure. When viewing from the left (from the positive xaxes), one sees that the wheel is rotating in a clockwise manner. The distance from the center of the wheel to the pivot point is 0.6 m. The wheel is a hoop of radius 0.5 m, and its shaft is horizontal.
Assume all of the mass of the system is located at the rim of the bicycle wheel. The acceleration of gravity is 9.8 m/s^{2} .
z
y
x
0.5 m m g
radius
Find the change in the precession angle after a 1.6 s time interval.
Correct answer: 8.695 ^{?}.
Explanation:
Let : m = 3 kg ,
ω = 2368 rev/min
= 2 π (2368 rev/min)
(60 s/min)
= 247.976 rad/s , b = 0.6 m , and
R = 0.5 m .
Overton, Mays – Midterm 3 – Due: Apr 6 2005, 10:00 pm – Inst: Turner 2
Basic Concepts:
→τ =
d L→ dt
003 (part 1 of 2) 10 points
A small puck of mass 27 g and radius
3. 14 cm slides along an air table with a speed
of 1.7 m/s. It makes a glazing collision with a larger puck of radius 34 cm and mass 66 g (ini tially at rest) such that their rims just touch. The pucks stick together and spin around af ter the collision.
Note: The pucks are disks which have a
Using the relation, ?L = τ ?t , where τ

The precession angle ?φ is
?φ = ?L
L
= τ ?t
L
is the
moments of inertia equal to 1 m r^{2}.
2
14 cm radius
+cm ω 
V 
ω 
27 g
L 34 cm
66 g
= m g b ?t m R2 ω
= g b ?t
R2 ω
= (9.8 m/s2) (0.6 m) (1.6 s) (0.5 m)2(247.976 rad/s)
= 0.151756 rad
Figure: The two pucks:
After the collisions the centerof


→τ = →b m →g , where →b is along the positive yaxis and →g is into the page, in the figure below. Therefore the direction of the torque
→τ is along the positive yaxis.
+x 
wheel 
L 
−x 
τ 
+y 
Viewed from Above
ofmass “+ cm”.
What is the angular momentum of the sys tem relative to the center of mass after the collision?
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