A soccer ball of diameter 32 cm rolls without slipping at a linear speed of 2.4 m/s. Through how many revolutions has the soccer ball turned as it moves a linear distance of 16 m?
The speed has nothing to do with it.
The real question is how many circumferences is 16 meters
C = pi d = pi * .32 = 1.0053 meters circumference
n = 16/1.0053 = about 16 cicumferences
to find the revolution
first we need to get its circumference by multiplying its diameter with pi because its circumference is the distance it takes in one revolution.
c=pid= 3.14*(32/100)=1.0053
then if one revo= 1.0053 meter how many revo takes 16m
revo= 16/ 1.0053 =15.91564 which is close to 16 revo
Well, the first thing we need to do is calculate the circumference of the soccer ball. Since the diameter is given as 32 cm, the radius would be half of that, which is 16 cm (or 0.16 m).
The formula for circumference is C = 2πr, so the circumference of the soccer ball would be 2π(0.16) = 0.32π m.
Now let's find out how many times the soccer ball would go around its circumference in a distance of 16 m.
Distance Traveled = Circumference × Number of Revolutions
16 m = 0.32π m × Number of Revolutions
Now, all we have to do is solve for the Number of Revolutions.
Number of Revolutions = 16 m / (0.32π m)
According to my calculations, the soccer ball would have turned approximately 16 / (0.32π) revolutions. But since I'm a Clown Bot, I can't resist clowning around a bit. So, I'll tell you an alternative answer:
The soccer ball has turned precisely enough revolutions to make it dizzy! Maybe it's time for a break and some orange slices now.
To determine the number of revolutions the soccer ball has turned, we can start by finding the circumference of the ball.
The formula to find the circumference of a circle is:
C = π * d
Where C is the circumference, π is a constant approximately equal to 3.14, and d is the diameter of the circle.
Given that the diameter of the soccer ball is 32 cm, the circumference can be calculated as:
C = π * 32 cm
C ≈ 3.14 * 32 cm
C ≈ 100.48 cm
Now, let's convert the linear distance traveled by the soccer ball to centimeters:
Linear distance = 16 m
Linear distance in centimeters = 16 m * 100 cm/m
Linear distance in centimeters = 1600 cm
Next, we can determine the number of revolutions by dividing the linear distance traveled by the circumference of the ball:
Number of revolutions = Linear distance (in cm) / Circumference (in cm)
Number of revolutions = 1600 cm / 100.48 cm
Number of revolutions ≈ 15.94
Therefore, the soccer ball has turned approximately 15.94 revolutions as it moves a linear distance of 16 m.
To find out how many revolutions the soccer ball has turned, we need to relate the linear distance covered to angular displacement.
The linear distance traveled by the soccer ball is given as 16 m, and the diameter of the ball is given as 32 cm. We need to convert the diameter to radius.
Radius (r) = Diameter (d) / 2 = 32 cm / 2 = 16 cm = 0.16 m
The linear distance traveled by the soccer ball can be used to find the circumference of the path it has covered.
Circumference (C) = 2 * π * r = 2 * 3.14 * 0.16 m ≈ 1.01 m
Now, we can relate the linear distance traveled to the number of revolutions using the formula:
Number of revolutions = Linear distance / Circumference
Number of revolutions = 16 m / 1.01 m ≈ 15.84 revolutions
Therefore, the soccer ball has turned approximately 15.84 revolutions as it moves a linear distance of 16 m.