A bicycle wheel is 30 inches in diameter.

a. To the nearest revolution,how many times will the wheel turn if the bicycle is ridden for 3 miles?
b. Suppose the wheel turns at a constant rate of 2.75 rev per second. What is the linear velocity in mph of a point on the tire?

c = pi*D = 3.14 * 30 = 94.2in. = 7.85ft = circumference.

3mi = 3mi * 5280ft/mi = 15840ft.

a. Rev = 15840ft / 7.85ft/rev = 2018.

b. V = 2.75rev/s * 7.85ft/rev * (1/5280)mi/ft * 3600s/h = 14.7mi/h.

a bicycle wheel is 63 cm in diameter. how many complete turns does it make in travelling 1 kilometer

128km

To solve these problems, we need to use some mathematical formulas related to the circumference and linear velocity of the bicycle wheel.

a. To find how many times the wheel will turn for a given distance, we can use the formula:

Number of revolutions = Distance / Circumference

The circumference of a circle is calculated as the diameter times π (pi), where π is approximately 3.14159.

Let's plug in the values into the formula:

Diameter = 30 inches
Circumference = Diameter × π

Circumference = 30 inches × 3.14159

Calculating the circumference, we get:

Circumference ≈ 94.2478 inches

Now, since the distance is given in miles, we need to convert the circumference into miles by dividing it by 63,360 (since there are 63,360 inches in a mile):

Circumference_in_miles ≈ 94.2478 inches / 63,360 inches/mile

Circumference_in_miles ≈ 0.0014848 miles

Finally, we can calculate the number of revolutions:

Number of revolutions ≈ Distance / Circumference_in_miles

Number of revolutions ≈ 3 miles / 0.0014848 miles

Calculating the number of revolutions, we get:

Number of revolutions ≈ 2019.4 revolutions (rounded to the nearest whole number)

Therefore, to the nearest revolution, the bicycle wheel will turn approximately 2019 times if the bicycle is ridden for 3 miles.

b. To find the linear velocity in mph (miles per hour) of a point on the tire, we can multiply the number of revolutions per second by the circumference in miles per revolution.

Linear velocity = Number of revolutions per second × Circumference_in_miles

Plugging in the given values:

Number of revolutions per second = 2.75 rev/sec
Circumference_in_miles ≈ 0.0014848 miles (from part a)

Calculating the linear velocity, we get:

Linear velocity ≈ 2.75 rev/sec × 0.0014848 miles/rev

Linear velocity ≈ 0.0039412 miles/sec

To find the velocity in miles per hour, we multiply it by 3,600 (since there are 3,600 seconds in an hour):

Linear velocity ≈ 0.0039412 miles/sec × 3,600 sec/hour

Calculating the linear velocity in miles per hour, we get:

Linear velocity ≈ 14.1871 mph

Therefore, the linear velocity of a point on the tire is approximately 14.1871 mph.