a string is wound a wheel of radius 20cm. how large is the angle through which the wheel must turn to unwind 30cm of the string.
C = pi*2r = 3.14 * 40 = 125.6 cm.
A = 360o/125.6cm * 30cm = 86o.
To find the angle through which the wheel must turn to unwind the string, we can use the relationship between the length of an arc and the radius of a circle. This relationship is given by the formula:
Length of arc = radius * angle in radians
Let's calculate the angle by substituting the given values into the formula:
Length of arc = 30 cm
Radius = 20 cm
We can rearrange the formula to solve for the angle:
Angle in radians = Length of arc / Radius
Plugging in the values, we get:
Angle in radians = 30 cm / 20 cm = 1.5 radians
Therefore, the wheel must turn through an angle of 1.5 radians to unwind 30 cm of the string.