Multiple Choice
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?
12. Rotational Kinematics
Rotational Position & Displacement
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While you drive, your tires, all of radius 0.40 m, rotate 10,000 times. How far did you drive, in meters?
A
5027 m
B
8667 m
C
12566 m
D
25132 m
Verified step by step guidance1
First, understand that the distance traveled by the car is related to the number of rotations of the tires and the circumference of the tires.
Calculate the circumference of one tire using the formula: \( C = 2\pi r \), where \( r \) is the radius of the tire. Here, \( r = 0.40 \) m.
Substitute the given radius into the formula to find the circumference: \( C = 2 \times \pi \times 0.40 \).
Determine the total distance traveled by multiplying the circumference of the tire by the number of rotations: \( \text{Distance} = C \times \text{number of rotations} \).
Substitute the values: \( \text{Distance} = (2 \times \pi \times 0.40) \times 10000 \) to find the total distance traveled in meters.
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