A typical record album is 12in in diameter and plays at 33 1/3 revolutions per min. What is the angular speed of a record album?
Can someone show me how to do this?? I'm so lost!!
33 1/3 revolutions per min
= 100/3 rpm
since 1 rotation (revolution) = 360° or 2π radians
the angular velocity = 100/3(360° per minute or 12 000°/min
in radians it would be 100/3(2π) rad/min = 200π/3 rad/min
of course if you wanted it per second, you would divide each of the above by 60
To find the angular speed of a record album, you need to convert the speed of revolution from revolutions per minute (RPM) to radians per second (rad/s).
Step 1: Convert revolutions per minute to revolutions per second:
Since there are 60 seconds in a minute, divide the given 33 1/3 RPM by 60 to get the revolutions per second.
33 1/3 RPM = (33 + 1/3) RPM = 33.3333 RPM
Angular speed (in revolutions per second) = 33.3333 RPM / 60 seconds = 0.5556 RPM/second
Step 2: Convert revolutions per second to radians per second:
To convert from revolutions to radians, use the conversion factor 2π radians = 1 revolution.
Multiply the angular speed (in revolutions per second) by 2π to get the angular speed in radians per second.
Angular speed (in radians per second) = 0.5556 RPM/second x 2π radians/1 revolution ≈ 3.4925 radians/second
So, the angular speed of a record album is approximately 3.4925 radians per second.
To find the angular speed of a record album, we can use the formula for angular speed:
Angular Speed = (2π × revolutions) / time
In this case, the time is given as 1 minute and the number of revolutions is 33 1/3. However, we first need to convert 33 1/3 into a decimal. To do this, we can convert the fraction into a decimal:
1/3 = 0.333 (approximately)
Now, we can substitute the values into the formula:
Angular Speed = (2π × 33.333) / 1
Simplifying the equation:
Angular Speed = 66.666π
Therefore, the angular speed of the record album is approximately 66.666π radians per minute.