A wheel is rotating at a rate of 2.5 revolutions every 3.6 s. Through what angle, in radians, does the wheel rotate in 1.0 s?
displacement=2.5rev/3.6sec * 2PIrad/rev * 1sec
2 pi radians/rev ( 2.5 rev /3.6 s)
= 4.36332313 radians/second
i dont understand :(
To find the angle in radians through which the wheel rotates in 1.0 second, we need to first determine the angle rotated in 3.6 seconds. We can then use this information to calculate the angle in 1.0 second.
Given:
- The wheel rotates at a rate of 2.5 revolutions every 3.6 seconds.
First, we need to find the angle rotated in 3.6 seconds.
1 revolution is equal to 2π radians.
If the wheel rotates 2.5 revolutions in 3.6 seconds, we can calculate the total angle rotated in radians:
Angle (in radians) = 2.5 revolutions * 2π radians/revolution
Angle = 2.5 * 2π radians
Angle ≈ 15.7 radians (rounded to one decimal place)
Now, we need to find the angle rotated in 1.0 second.
We know that the angle is directly proportional to time.
Angle in 1 second = (Angle in 3.6 seconds) / (3.6 seconds) * (1 second)
Angle in 1 second = 15.7 radians / 3.6 seconds * 1 second
Angle in 1 second ≈ 4.4 radians (rounded to one decimal place)
Therefore, the wheel rotates approximately 4.4 radians in 1.0 second.