The front sprocket off a bicycle is 12 centimeters and the rear one is 5 centimeters. What is the linear velocity of the chain around the back sprocket?
if the bicycle has tires that have a 38 centimeter diameter, how fast is the bicycle moving?
400pi m/s
To find the linear velocity of the chain around the back sprocket, we need to calculate the circumference of the back sprocket first.
The circumference of a circle can be found using the formula: C = π * d, where C is the circumference and d is the diameter.
Given that the rear sprocket has a diameter of 5 centimeters, the circumference of the back sprocket is:
C = π * 5 = 15.7 centimeters.
Now, to find the linear velocity of the chain around the back sprocket, we need to multiply the circumference of the back sprocket by the rotational speed (in revolutions per minute) of the back sprocket.
Let's assume the rotational speed of the back sprocket is x revolutions per minute.
The linear velocity of the chain is then given by the formula: V = C * x, where V is the linear velocity.
Now, to find how fast the bicycle is moving, we need to consider the relationship between the linear velocity of the chain and the linear velocity of the bicycle.
The linear velocity of the bicycle is equal to the linear velocity of the chain multiplied by the ratio of the circumference of the tire to the circumference of the back sprocket.
Given that the diameter of the tire is 38 centimeters, the circumference of the tire is:
C = π * 38 = 119.4 centimeters.
Let's assume the linear velocity of the bicycle is y centimeters per minute.
Therefore, we have the equation: y = V * (C_tire / C_sprocket), where C_tire is the circumference of the tire and C_sprocket is the circumference of the back sprocket.
Substituting the values, we get: y = V * (119.4 / 15.7).
Now, we can calculate the linear velocity of the chain and then use it to find the speed of the bicycle.