Open Question
FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?
12. Rotational Kinematics
Rotational Position & Displacement
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An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through?
BONUS:How many complete revolutions does it make?
A
33.3°
B
488°
C
987°
D
1908°
Verified step by step guidance1
First, understand that the problem involves circular motion. The object moves around a circle, so we need to relate the distance traveled to the circle's circumference.
Calculate the circumference of the circle using the formula: , where is the radius of the circle. Substitute m for .
Determine how many complete revolutions the object makes by dividing the total distance traveled by the circumference: , where is the total distance of m.
Convert the number of revolutions into degrees. Since one complete revolution is degrees, multiply the number of revolutions by to find the total degrees traveled.
For the bonus, use the number of complete revolutions calculated in step 3 to determine how many full circles the object completes.
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