PRACTICE IT A compact disc rotates from rest up to an angular speed of 33.5 rad/
ID: 1288932 • Letter: P
Question
PRACTICE IT
A compact disc rotates from rest up to an angular speed of 33.5 rad/s in a time of 0.893 s.
(a) What is the angular acceleration of the disc, assuming the angular acceleration is uniform?
37.5 rad/s2
(b) Through what angle does the disc turn while coming up to speed?
15 rad
(c) If the radius of the disc is 4.45 cm, find the tangential speed of a microbe riding on the rim of the disc.
1.49 m/s
(d) What is the magnitude of the tangential acceleration of the microbe at the given time?
1.67 m/s2
Use the values from PRACTICE IT to help you work this exercise.
(a) What are the angular speed and angular displacement of the disc 0.310 s after it begins to rotate?
??= ???rad
(b) Find the tangential speed at the rim at this time.
m/s ???
All I need help with is finding the last two problems...everything else I am fine with. Please help. Thanks!!
?= 11.6 rad/s??= ???rad
Explanation / Answer
his is a conservation of angular momentum problem
Initially the system is at rest so L(total) = 0
Since there is no external forces acting on the system (everything that happens is perpendicular to gravity so this can be ignored and there is no friction) L(total) is constant and hence remains 0.
After motion starts:
The angular momentum of the man wrt the axis of the disc is
L(man) = m*r*v
Where m is the mass of the man, r is the distance of the man to the axis of the disc and v is the tangental speed of the man relative to the ground.
and the angular momentum of the disc is
L(disc) = I*w
Where I is the moment of inertia of the disc and I = (1/2)*M*R^2 ( here M is mass of the disc and R is the radius of the disc) and w is the angular velocity of the disc.
From the conservation of angular momentum
L(man) + L(disc) = 0
L(man) = -L(disc)
m*v*r = -(1/2)*M*R^2*w
So
w = -(2*m*v*r) / (M*R^2)
w=?
So the angular speed is rad/s
The minus sign is an indication that the disc is rotating in the opposite direction to the motion of the man.
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