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I am not going to do your experimental laboratory but I will answer the two following theoretical questions.
We know that a full circle has a circumference equal to:
`P =2*pi*R =R*theta`
where angle `theta` is measured in radians.
Since a full circle represents an angle at center of 360 degree, from the above relation for the circle circumference, it results that `2*pi` radians are equivalent to `360` degrees. Therefore `1` radian is equivalent to an angle in degree of:
`1 rad =360/(2*pi) =360/(2*3.1415927) =57.2958 =57.296 degree`
For `n` radians we have a corresponding angle measured in degrees of
`n (rad) =(360*n)/(2*pi) (degree) =n*57.296 (degree)`
Answer: 1 radian is equivalent to 57.296 degree
Since `2*pi ` radians correspond for `360` degree, for ` ``30 =360/12 degree`, correspond `(2*pi)/12 =pi/6` radians.
The length of arc from a circle having radius `R=1.5 m` that corresponds to an angle` ` at center of
`theta= 30 degree =pi/6 rad` is
`L =R*theta =1.5*pi/6 =0.78540 m= 0.785 m`
(Again we should emphasize that in the above relation the angle theta is measured in radians).
Answer: the length of the path of the object on the circle is 0.785 m
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