Open Question
(II) A child rolls a ball on a level floor 3.1 m to another child. If the ball makes 12.0 revolutions, what is its diameter?
12. Rotational Kinematics
Rotational Position & Displacement
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A car travels a total of 2,000 m and 1140° around a circular path, starting from 0° . What is the radius of the circular path?
BONUS:How far (in degrees) from 0° does the car end up?
A
1.754 m
B
100.5 m
C
780.8 m
D
2000 m
Verified step by step guidance1
First, understand that the car travels along a circular path, covering a total distance of 2,000 meters. This distance is the arc length of the circle.
The car travels 1,140° around the circle. To find the radius, we need to convert this angle from degrees to radians because the formula for arc length uses radians. Use the conversion: radians = degrees × (π/180).
Calculate the angle in radians: 1,140° × (π/180) = θ radians.
Use the formula for arc length, which is: arc length = radius × angle in radians. Rearrange this formula to solve for the radius: radius = arc length / angle in radians.
Substitute the known values into the formula: radius = 2,000 m / θ radians. This will give you the radius of the circular path.
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