Respuesta :
1) 1 rpm corresponds to 1 revolution per minute. Since 1 minute = 60 seconds, 33 rpm are equal to
[tex] \frac{33~r/m}{60~s/m} = 0.55~rps[/tex]
So, 0.55 revolutions per second.
2) 1 revolution corresponds to [tex]360^{\circ}[/tex], which is equal to [tex]2\pi[/tex] radians. So we can write the following proportion:
[tex]1~rps : 2\pi~rad/s = 0.55~rps : x[/tex]
and from this we can find x, the angular speed in rad/s:
[tex]x= \frac{2\pi ~rad/s \cdot 0.55~rps}{1~rps} =3.45~rad/s[/tex]
[tex] \frac{33~r/m}{60~s/m} = 0.55~rps[/tex]
So, 0.55 revolutions per second.
2) 1 revolution corresponds to [tex]360^{\circ}[/tex], which is equal to [tex]2\pi[/tex] radians. So we can write the following proportion:
[tex]1~rps : 2\pi~rad/s = 0.55~rps : x[/tex]
and from this we can find x, the angular speed in rad/s:
[tex]x= \frac{2\pi ~rad/s \cdot 0.55~rps}{1~rps} =3.45~rad/s[/tex]
The angular speed of rotation of the record on the turntable is [tex]\boxed{3.45\text{ rad/sec}}[/tex].
Explanation:
The angular speed of a body is the speed of rotation as which the body completes the circle. It is defined as the rate of change of angular displacement of a body.
The angular speed of a body in terms of rpm is the measure of the number of rotations performed by the body in time interval of one minute.
The angular displacement of a body in one complete revolution is [tex]2\pi[/tex] and the number of seconds in an interval of one minute is [tex]60\text{ s}[/tex].
Write the conversion factor for the conversion of rpm into the angular velocity.
[tex]\omega=(rpm)\times\dfrac{2\pi}{60}[/tex]
Substitute the value of [tex]rpm[/tex] in above expression.
[tex]\begin{aligned}\omega&=(33)\times\dfrac{2\pi}{60}\text{ rad/sec}\\&=\dfrac{66\pi}{60}\text{ rad/sec}\\&=3.45\text{ rad/sec}\end{aligned}[/tex]
Thus, the angular speed of rotation of the record on the turntable is [tex]\boxed{3.45\text{ rad/sec}}[/tex].
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Circular Motion
Keywords:
record, rotates, turntable, rpm, rotation per minute, rad/sec, angular speed, second, velocity, rate of change, displacement.
