A wheel is rotating at a rate of 2.2 revolutions every 3.5 s. Through what angle, in radians, does the wheel rotate in 1.0
Angular displacement=angularspeed*time
angular speed has to be in radians/sec, and time in seconds.
To find the angular displacement in radians, we need to convert the given information into the appropriate units.
First, let's convert the rotation rate from revolutions to radians. Since 1 revolution is equal to 2π radians, we can multiply the rotation rate by 2π to convert it to radians per second.
Given: Rotation rate = 2.2 revolutions / 3.5 seconds
Conversion: 2.2 revolutions * 2π radians / 1 revolution = 4.4π radians / 3.5 seconds
Now we have the angular speed in radians per second.
Next, we multiply the angular speed by the time to calculate the angular displacement.
Given: Time = 1.0 second
Angular displacement = 4.4π radians / 3.5 seconds * 1.0 second
Simplifying the equation:
Angular displacement = 4.4π radians / 3.5
Now we can calculate the angular displacement in radians:
Angular displacement ≈ 1.257π radians
Therefore, the wheel rotates through an angle of approximately 1.257π radians in 1.0 second.