carnival has a ferris wheel

Question

carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

Answer 1

Hello,

The first part of the question asks for the linear speed of a point on the edge of the Ferris Wheel. Speed is calculated by dividing the distance traveled by the time. s = d/t

The distance the point on the edge travels in one revolution is equal to the length of the circumference (the distance around the circle). The formula for circumference is C = πd, where C is the circumference and i is the diameter. Therefore,

C = πd

C = π(80)

C ≈ 251.3 feet

If the time for a complete revolution is 75 seconds, the speed is then

s = d/t

s = 251.3 ft / 75 sec

s = 3.35 ft/sec

Now, for the 2nd part of the question. What is the angular speed?

Angular speed is simply the rotation angle divided by the time.

Since one revolution is 2π radians and this is completed in 75 seconds, we divide 2π by 75 and get

0.084 radians/second.

Hope this helps! :)

Answer 2

Hi Haya A.,

Linear speed is the change in distance over the change in time (example mph or miles/hour).

The linear speed of a wheel is the distance the wheel travels over time. The distance a wheel travels for one revolution is its circumference (C = π*d = 2*π*r). So the linear speed of a wheel is v = π*d / t, where d = diameter and t = time for one revolution.

The linear speed of the Ferris wheel is π*80 / 75 ft/s.

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Angular speed is the angular displacement over time. For any wheel it takes 2π radians or 360^o to make one revolution. The angular speed is then ω = 2π / t, with t = the time it takes to make one revolution.

For the Ferris wheel the angular speed is ω = 2π / 75 rads/s.

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You can see how angular speed and linear speed are related, v = ω*r

I hope this helps, Joe.

Answer 3

We start with what we know:

diameter: d=80

for linear speed, we need to know the speed of the outside of the circle. Speed is distance divided by time.

The distance all the way around the outside of a circle is called the circumference. the formula is C=π x d

C = 80 * π

C ≈ 251.327

As mentioned earlier, speed is distance divided by time. We are given that 1 revolution takes 75 seconds.So, we travel 251.327 feet in 75 seconds.

251.327 ft ÷ 75 s ≈3.351 feet per second.

For angular speed, we need the total angle traveled (in radians) and the total time (still 75 seconds).

Angular speed is total angle traveled divided by total time. The number of radians in a circle is 2*π.

2*π ≈ 6.283 radians

So, total angle divided by total time is:

6.283 radians ÷ 75 s ≈ 0.0838 radians per second