Question

A boy rides his bicycle 2.25 km. The wheels have radius 30.0 cm. What is the total angle the tires rotate through during his trip

Answer 1

The total angle the tires rotate through during the boy's trip is approximately 7500.24 radians.

Step-by-step explanation:

To find the total angle the tires rotate through during the boy's trip, we need to calculate the number of revolutions made by the tires. The circumference of a circle is given by the formula C = 2πr, where r is the radius and π is a constant value of approximately 3.14. In this case, the radius of the bicycle wheels is 30.0 cm, so the circumference is C = 2π(30.0 cm) = 60.0π cm.

To convert the distance the boy travels from kilometers to centimeters, we multiply the given distance by 100,000 since there are 100,000 centimeters in a kilometer. Therefore, the distance the boy travels in centimeters is 2.25 km × 100,000 cm/km = 225,000 cm.

The number of revolutions made by the tires can be calculated using the formula revolutions = distance / circumference. Substituting the known values, we get revolutions = 225,000 cm / (60.0π cm). Evaluating this expression, we find that the number of revolutions is approximately 1194.77 revolutions.

The total angle the tires rotate through, denoted by θ, can be found using the formula θ = 2π × revolutions. Substituting the value for revolutions, we get θ = 2π × 1194.77, which is approximately 7500.24 radians.

Answer 2

The angle can be found using the formula angle = 2π × number of revolutions. Plugging in the values, we get the answer: angle = 7500π radians.

Step-by-step explanation:

To find the total angle the tires rotate through, we first need to calculate the distance the tires travel. The distance can be calculated using the formula distance = circumference × number of revolutions.

The circumference of a circle is given by 2πr, where r is the radius. In this case, the radius is given as 30.0 cm, so the circumference is 2π(30.0 cm) = 60π cm.

Since the boy rides his bicycle for 2.25 km, we convert this distance to cm: 2.25 km × 100,000 cm/km = 225,000 cm. Now, we can calculate the number of revolutions: 225,000 cm ÷ 60π cm/rev.

Finally, the total angle the tires rotate through can be found using the formula angle = 2π × number of revolutions. Plugging in the number of revolutions, we get the answer:

angle = 2π × (225,000 cm ÷ 60π cm/rev) = 7500π radians