Please help with these problems. Thanks!
Suppose the circumference of a bicycle wheel is 2 meters. If it rotates at 1 revolution per second when you are riding the bicycle, then your speed will be?
Suppose you're on a Ferris wheel at a carnival, seated 10 m from the Ferris wheel's axis. If you make a complete rotation each minute, your linear speed is?
62.8 m/min
To calculate the speed in the given scenarios, we need to understand the relationship between speed, distance, and time.
1. For the bicycle wheel problem:
The circumference of the wheel is given as 2 meters. We know that the distance traveled in one revolution is equal to the circumference of the wheel. Since the bicycle wheel rotates at 1 revolution per second, it means that every second, the distance traveled is equal to the circumference of the wheel.
Therefore, the speed of the bicycle is equal to the circumference of the wheel, which is 2 meters per second.
2. For the Ferris wheel problem:
In this scenario, we need to find the linear speed, which is the speed at which a point on the Ferris wheel moves in a straight line.
We are given that a complete rotation takes one minute. To find the speed, we need to convert the time taken from minutes to seconds because the circumference of the Ferris wheel is given in meters.
There are 60 seconds in one minute, so the time taken for one rotation is 60 seconds. With a distance of 10 meters traveled in one rotation, we can calculate the speed by dividing the distance traveled by the time taken:
Speed = Distance / Time = 10 meters / 60 seconds
Simplifying that, we find that the linear speed is approximately 0.167 meters per second.
Therefore, if you are seated 10 meters from the Ferris wheel's axis and make a complete rotation each minute, your linear speed would be approximately 0.167 meters per second.
Remember, these calculations are based on the assumptions provided in the problems.