Question

In a Beams ultracentrifuge, the rotor is suspended magnetically
in a vacuum. Since there is no mechanical connection to the rotor,
the only friction is the air resistance due to the few air
molecules in the vacuum. If the rotor is spinning with an angular
speed of 5.00 × 10^{5} rad/s and the driving force is
turned off, its spinning slows down at an angular rate of magnitude
0.400 rad/s^{2}. The rotor of the Beams ultracentrifuge is
a rod 26.4 cm long, turning about a perpendicular axis through its
center.

For a point at the end of the rotor, find the initial speed.

For a point at the end of the rotor, find the magnitude of the tangential acceleration component.

For a point at the end of the rotor, find the maximum radial acceleration component.

Answer #1

w_{o} = initial angular speed = 5 x 10^{5}
rad/s

r = radius = length of the rod = 26.4 cm = 0.264 m

v_{o} = initial linear speed

initial linear speed is given as

v_{o} = r w_{o}

v_{o} = (0.264) (5 x 10^{5} )

v_{o} = 1.32 x 10^{5} m/s

= angular acceleration = 0.4 rad/s^{2}

a = linear acceleration

Linear acceleration is given as

a = r

a = (0.264) (0.4)

a = 0.1056 m/s^{2}

radial acceleration is given as

a_{r} = v_{o}^{2}/r

a_{r} = (1.32 x 10^{5} )^{2}/(0.264)

a_{r} = 6.6 x 10^{10} m/s^{2}

At a time t = 3.10 s , a point on the rim of a wheel
with a radius of 0.210 m has a tangential speed of 51.0 m/s as the
wheel slows down with a tangential acceleration of constant
magnitude 10.6 m/s2 .
Calculate the wheel's constant angular
acceleration. rad/s^2
Calculate the angular velocity at t = 3.10 s. rad/s
Calculate the angular velocity at t=0. rad/s
Through what angle did the wheel turn between t=0 and
t = 3.10...

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(a) Calculate the wheel's constant angular acceleration.
[-52 rad/s2]
(b) Calculate the angular velocities at t = 2.55 s and
t = 0.
ω2.55 s
= [ ] rad/s
ω0
= [ ] rad/s
(c) Through what angle did the wheel turn between t =...

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HINT
An illustration shows the horizontal initial position and
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A disk with mass m = 10.3 kg and radius R = 0.34 m begins at
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1)
What is the angular acceleration of the disk?
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2)
What is the angular displacement over the 16.8 s?
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3)
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4)
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J
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A disk with mass m = 8.5 kg and radius R = 0.35 m begins at rest
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c) What is the moment of inertia of the disk?
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e) What is the tangential...

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