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

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Chapter1: Units, Trigonometry. And Vectors
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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
Transcribed Image Text: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
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
Transcribed Image Text: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
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