An old-fashioned vinyl record is designed to turn at 33 rev/min. Find the average angular velocity. Express your answer in radians per second to two significant figures. ΑΣΦ Submit Request Amewer ? rad/s
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![Let's begin with the angular acceleration of a compact
disk (CD). To play music the CD must rotate at high
speed while a laser reads data encoded in a spiral
pattern on the disk. The disc has radius
R = 6.0 cm = 0.060 m; when data are being read, it
spins at 7200 rev/min. What is the CD's angular
velocity w in radians per second? How much time is
required for it to rotate through 90° ? If it starts from rest
and reaches full speed in 4.0 s, what is its average
angular acceleration?
Figure
02
Δθ = 900
w= 7200 rev/min
R = 0.060 m
1 of 1
0₁
SOLVE To convert the disc's angular velocity w to radians per second, we multiply by (1 min/60 s) and by (2π rad/1 rev):
(1 min) (2π rad
1 rev
From the definition of angular acceleration (Cav
rest), the average angular acceleration is
Part A - Practice Problem:
W=
From the definition of angular velocity (w = A0/At), we find the time At for the disc to turn through 90° (π/2 rad):
π/2 rad
754 rad/s
Aw/At), if the disc reaches a final angular velocity of 754 rad/s in 4.0 s (starting from
7200 rev
1 min
Submit
ΑΣΦ
Request Answer
At =
=
ΔΘ
day =
7200 rev
1 min
Δω
At
REFLECT A typical circular (table or radial-arm) saw used in wood-working shops runs at 3600 rev/min and reaches full speed about 1 s
after it is turned on. The radius of a typical blade is 12 cm. Note, however, that the radius is not needed to determine the angular acceleration
calculation. The angular acceleration is about twice that for the CD.
I ?
= 754 rad/s
754 rad/s
4.0 s
An old-fashioned vinyl record is designed to turn at 33 rev/min. Find the average angular velocity.
Express your answer in radians per second to two significant figures.
= 0.0021 s = 2.1 ms
rad/s
= 189 rad/s²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57c5c9b-acb3-4a3d-a39b-55eeff7ee4ad%2Fd05ce537-fd1a-47e2-b7d3-f81c8e7775b9%2Ff5xehpr_processed.png&w=3840&q=75)
![Part B - Practice Problem:
Find the angular acceleration of the record if it spins through six full rotations before coming to a stop when the record player is turned off.
Express your answer in radians per second squared to two significant figures.
ΑΣΦ
rad/s²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57c5c9b-acb3-4a3d-a39b-55eeff7ee4ad%2Fd05ce537-fd1a-47e2-b7d3-f81c8e7775b9%2Fvkctb07_processed.png&w=3840&q=75)
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