CE Predict/Explain A disk and a hoop (bicycle wheel) of equal radius and mass each have a string wrapped around their circumferences Hanging from the strings, halfway between the disk and the hoop, is a block of mass m, as shown in Figure 11-56. The disk and the hoop are free to rotate about their centers When the block is allowed to fall does it stay on the center line, move toward the right, or move toward the left'? (b) Choose the best explanation from among the following: Figure 11-56 Problem 71 I. The disk is harder to rotate and hence its angular acceleration is less than that of the wheel. II. The wheel has the greater moment of inertia and unwinds more slowly than the disk. III. The system is symmetric, with equal mass and radius on either side.
CE Predict/Explain A disk and a hoop (bicycle wheel) of equal radius and mass each have a string wrapped around their circumferences Hanging from the strings, halfway between the disk and the hoop, is a block of mass m, as shown in Figure 11-56. The disk and the hoop are free to rotate about their centers When the block is allowed to fall does it stay on the center line, move toward the right, or move toward the left'? (b) Choose the best explanation from among the following: Figure 11-56 Problem 71 I. The disk is harder to rotate and hence its angular acceleration is less than that of the wheel. II. The wheel has the greater moment of inertia and unwinds more slowly than the disk. III. The system is symmetric, with equal mass and radius on either side.
CE Predict/Explain A disk and a hoop (bicycle wheel) of equal radius and mass each have a string wrapped around their circumferences Hanging from the strings, halfway between the disk and the hoop, is a block of mass m, as shown in Figure 11-56. The disk and the hoop are free to rotate about their centers When the block is allowed to fall does it stay on the center line, move toward the right, or move toward the left'? (b) Choose the best explanation from among the following:
Figure 11-56 Problem 71
I. The disk is harder to rotate and hence its angular acceleration is less than that of the wheel.
II. The wheel has the greater moment of inertia and unwinds more slowly than the disk.
III. The system is symmetric, with equal mass and radius on either side.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
9) In the problem above, what is the final center of mass velocity of the
disk after it falls a total height h? Assume it starts falling from rest.
Hint: Use conservation of energy
A) | Voom |= /2gh
B) | Vcom = Vgh
(C) Vcom
Vi gh
D) | Vcom |= Vgh
E) Vcom
%3D
VA gh
F) | Vcom |= Vgh
%3D
7) A non-rotating uniform hoop of radius kb and mass m is dropped onto a rotating uniform disk of
radius b and mass 3m. If the disk is initially rotating with angular velocity @,, what is w, after
friction makes two objects rotate with the same angular velocity? Assume the central axes of both
objects always lie exactly along the same axis of rotation.
XA) @, =0,
B) @, = 0,
C) @, =0,
General c.o.m.
Moments
MR?
I hoop of
mass M,
radius R
%3D
Dinsction
Idisk of =MR
force
mass M
radius R
E)
Зт, о,
17-89. The "Catherine wheel" is a firework that consists of
a coiled tube of powder which is pinned at its center. If the
powder burns at a constant rate of 20 g/s such as that the
exhaust gases always exert a force having a constant
magnitude of 0.3 N, directed tangent to the wheel, determine
the angular velocity of the wheel when 75% of the mass is
burned off. Initially, the wheel is at rest and has a mass of
100 g and a radius of r=75 mm. For the calculation, consider
the wheel to always be a thin disk.
Co
0.3 N
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