A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center, as shown in the figure below. The linear speed of a passenger on the rim is constant and equal to 6.60 m/s.

What is the magnitude of the passenger's acceleration as she passes through the lowest point in her circular motion?

What is the magnitude of the passenger's acceleration as she passes through the highest point in her circular motion?

How much time does it take the Ferris wheel to make one revolution?

The linear speed is 6.6m/s. Determine the circumference of the wheel and how long it take the wheel to make a revolution, i.e., the wheel's angular velocity. Then use angular acceleration a=v^2/r.

The acceleration going up should be some kind of difference and the accel. coming down should be a sum. I'll let you figure it out.

To find the magnitude of the passenger's acceleration as she passes through the lowest point, we can use the formula for centripetal acceleration, which is given by:

a = v^2 / r

where "v" is the linear speed of the passenger on the rim and "r" is the radius of the Ferris wheel.

Substituting the given values, we have:

a = (6.60 m/s)^2 / 14.0 m

a ≈ 3.08 m/s^2

Therefore, the magnitude of the passenger's acceleration as she passes through the lowest point is approximately 3.08 m/s^2.

To find the magnitude of the passenger's acceleration as she passes through the highest point, we will use the same formula for centripetal acceleration. Since the linear speed is constant, the magnitude of the acceleration will remain the same. So, the magnitude of the acceleration at the highest point is also approximately 3.08 m/s^2.

To determine how long it takes the Ferris wheel to make one revolution, we need to find its angular velocity. The angular velocity (ω) is related to the linear speed (v) and the radius (r) by the equation:

ω = v / r

Substituting the given values, we have:

ω = 6.60 m/s / 14.0 m

ω ≈ 0.471 rad/s

The time taken for one revolution (T) is given by the formula:

T = 2π / ω

Substituting the value of ω, we have:

T = 2π / 0.471 rad/s

T ≈ 13.36 s

Therefore, it takes the Ferris wheel approximately 13.36 seconds to make one revolution.