A bicycle with 0.80 -diameter tires is coasting on a level road at 5.6 . A small blue dot has been painted on the tread of the rear tire.
a)What is the angular speed of the tires?
b)What is the speed of the blue dot when it is 0.80 above the road?
c)What is the speed of the blue dot when it is 0.40 above the road?
i just need to chec my answer, would be greatly appreciated :)
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a) To find the angular speed of the tires, we can use the formula:
angular speed = linear speed / radius
Given that the diameter of the tires is 0.80 m, we can calculate the radius by dividing the diameter by 2:
radius = 0.80 m / 2 = 0.40 m
The linear speed of the bike is given as 5.6 m/s. Substituting these values into the formula, we get:
angular speed = 5.6 m/s / 0.40 m = 14 rad/s
Therefore, the angular speed of the tires is 14 rad/s.
b) To find the speed of the blue dot when it is 0.80 m above the road, we can use the fact that all points on the tire have the same angular speed. Since the entire circumference of the tire is covered in one rotation, the distance traveled along the circumference is equal to 2π times the radius of the tire.
circumference = 2π × radius
= 2π × 0.40 m
≈ 2.51 m
Therefore, for every rotation of the tire, the blue dot travels a distance of 2.51 m. Since the angular speed is 14 rad/s, the time it takes for one rotation is:
time = 1 rotation / angular speed
= 1 / 14 s
Now, to find the speed of the blue dot when it is 0.80 m above the road, we can use the formula:
speed = distance / time
Substituting the values, we get:
speed = 0.80 m / (1 / 14 s)
= 11.2 m/s
Therefore, the speed of the blue dot when it is 0.80 m above the road is 11.2 m/s.
c) We can use the same approach as in part b to find the speed of the blue dot when it is 0.40 m above the road. The distance traveled along the circumference of the tire is still 2.51 m. Since the angular speed is the same, the time for one rotation remains unchanged:
time = 1 rotation / angular speed
= 1 / 14 s
Using the formula for speed, we have:
speed = 0.40 m / (1 / 14 s)
= 5.6 m/s
Therefore, the speed of the blue dot when it is 0.40 m above the road is 5.6 m/s.
Please note that these are the correct answers based on the given values, but always double-check your calculations to ensure accuracy.
a. 14 rad/s
b. 11.2 m/s
c. 5.6 m/s