Question

A centrifuge is rotating at 4700 RPM in a clockwise direction
when the power is turned off. It slows to a stop in 63 seconds. In
a coordinate system where the rotation is occurring in the x, y
plane and the z-axis points up away from the table,

a) What angular acceleration does the centrifuge experience while
slowing down? (Assume constant acceleration and pay attention to
the sign.) [ , , ]
rad/s^{2}

b) How many rotations does it complete during that time?

c) How many rotations has it completed 31.5 seconds after it began
slowing down?

Answer #1

A really old phonograph turntable, rotating at 78 rpm, slows
down and stops in 30 sec after the motor is turned off. (a) Find
its (uniform) angular acceleration. (b) How many revolutions did it
make in this time?

A 70.0-cm diameter flywheel is initially rotating clockwise at
100 rpm. It then undergoes a constant counterclockwise angular
acceleration of 2.50 radians per square second for 5.00
seconds.
a) What is the magnitude of the initial angular velocity in units
of radians per second?
b) What are the magnitude and direction of the final angular
velocity of the flywheel at the end of the 5.00 second interval in
units of rad/s?
c) What is the magnitude of the net angle...

When an old LP turntable was revolving at 33 1/3 rpm, it was
shut off and uniformly slowed down and stopped in 5.5 seconds.
(a) What was the magnitude of its angular acceleration (in
rad/s2) as it slowed down?
(b) Through how many revolutions did it turn while stopping?

A bicycle wheel is rotating at 46 rpm when the cyclist begins to
pedal harder, giving the wheel a constant angular acceleration of
0.50 rad/s^2.
What is the wheel's angular velocity, in rpm, 7.0 s later?
(Express your answer to two significant figures and include the
appropriate units.)
How many revolutions does the wheel make during this time?
(Express your answer to two significant figures.)

A body is initially (at t=0s) rotating about a z-axis as shown
below. Its initial angular speed is 8.50 rad/s. It's rotation is
slowing at a constant rate of 0.150 rad/s^2. a) How long does it
take to stop? b) How many revolutions did it make in this time
period? c) If the point shown is 17.0 cm from the z-axis, what was
the initial speed at this point and what was the initial
acceleration magnitude at this point?

Disc jockeys (DJs) use a turntable in applying their trade,
often using their hand to speed up or slow down a disc record so as
to produce a desired change in the sound. Suppose DJ Trick wants to
slow down a record initially rotating clockwise (as viewed from
above) with an angular speed of 32.1 rpm to an angular speed of
23.3 rpm. The record has a rotational inertia of
0.012 kg · m2
and a radius of 0.15 m....

A wheel at rest is accelerated with uniform angular acceleration
4.6 rad/s2. How many revolutions does it take for the wheel to
achieve 857 rev/min?
A child is sitting a distance 8 m from the center of a
merry-go-round that is 18.6 m in diameter. If the merry-go-round
makes 8.8 rev/min, what is the velocity of the child in m/s?
An object is in circulation motion at a speed of 499 rad/sec
when it begins to slow down at a...

Assessment
Identify the Variables!
In rotational kinematics - the variables are:
t = time, which is measured in s (for seconds)
θ = angle = what angle did the object turn thru, usually
measured radians
ωO = initial angular velocity = the rotational speed
of the object at the beginning of the problem, which is measured in
rad/s
ω = final angular velocity = the rotational speed of the object
at the end of the problem, which is measured in...

A child pushes her friend (m = 25 kg) located at a radius r =
1.5 m on a merry-go-round (rmgr = 2.0 m, Imgr
= 1000 kg*m2) with a constant force F = 90 N applied
tangentially to the edge of the merry-go-round (i.e., the force is
perpendicular to the radius). The merry-go-round resists spinning
with a frictional force of f = 10 N acting at a radius of
1 m and a frictional torque τ = 15 N*m...

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