a salt shaker is sitting 4cm from the center of a lazy susan. phoebe small spins the lazy susan through an angle of 120.
how do i set this up to find how many radians the shaker turned?
120 deg * 2pi rad / 360 deg = ?
To find the number of radians the salt shaker turned, you can use the formula:
θ = s/r
Where:
θ represents the angle in radians
s is the arc length (distance) traveled by the salt shaker
r is the radius (distance) from the center of rotation to the salt shaker
In this case, the salt shaker is sitting 4 cm from the center of the lazy susan, so the radius, r, is 4 cm.
The arc length, s, can be determined using the formula:
s = r × θ
If Phoebe Small spins the lazy susan through an angle of 120 degrees, you need to convert this angle to radians. Since there are π radians in 180 degrees, you can use the following conversion factor:
120 degrees × π radians / 180 degrees = 2/3π radians
Now, let's substitute the values into the formula:
θ = s/r
θ = (4 cm) × (2/3π radians) / (4 cm)
θ = 2/3π radians
Therefore, the salt shaker turned by an angle of 2/3π radians.