a motor turns 21.6 revolutions in 0.75 second. what is the angular speed of the motor in rpm? in radians per second?
rpm = 21.6 rev/(0.75/60 min)= 60*21.6/0.75 = ___
rad/s = (21.6 rev)*(2 pi rad/rev)/0.75 s
= ____
To find the angular speed of the motor, we need to first understand that angular speed represents the rate at which the motor rotates. It is usually measured in revolutions per minute (rpm) or radians per second (rad/s).
Given:
- Number of revolutions turned by the motor = 21.6 revolutions
- Time taken to turn those revolutions = 0.75 seconds
To find the angular speed in rpm:
1. Divide the number of revolutions by the time taken to get the angular speed in revolutions per second.
Angular speed (in revolutions per second) = Number of revolutions / Time = 21.6 revolutions / 0.75 seconds.
2. Multiply the angular speed in revolutions per second by 60 to convert it to revolutions per minute (rpm).
Angular speed (in rpm) = Angular speed (in revolutions per second) * 60.
To find the angular speed in radians per second:
1. Convert the number of revolutions to radians by multiplying it by 2π (since 1 revolution = 2π radians).
Number of radians = Number of revolutions * 2π = 21.6 revolutions * 2π.
2. Divide the number of radians by the time taken to get the angular speed in radians per second.
Angular speed (in radians per second) = Number of radians / Time = (21.6 revolutions * 2π) / 0.75 seconds.
Now, we can calculate the angular speed in both rpm and radians per second using the given values and formulas.