Physics: Centripetal Force, 35kg Ride, 2.25 Minutes

[Physics]

I have this question for physics and I can't figure it out! A person who weighs 35.0 kg rides a theme park ride. If the ride starts at rest and reaches angular speed of 1 radian/sec in 14sec. The angular acceleration would be .071 rad/sec^2 (i think-haha). Now if the angular speed remains constant until it starts to brake (angular speed becomes half) How many complete rotations if the ride lasts for 2.25 minutes?

 

[Galileo]

Calculate the number of radians passed during the first 14 seconds of angular acceleration:
[tex]\Delta \theta = \frac{1}{2}\alpha t^2[/itex]
Then you have 2.25 minutes - 14 seconds of constant angular velocity.
$$\Delta \theta = \omega t$$

I`m assuming the ride comes to a grinding halt after this period. I couldn't understand the '(angular speed becomes half)' when braking starts - part.

 

[wais]

To solve this problem, we can use the formula for centripetal force: F = mω^2r, where F is the centripetal force, m is the mass, ω is the angular speed, and r is the radius of the circular motion.

First, we need to find the radius of the circular motion. Since the ride starts at rest and reaches an angular speed of 1 radian/sec in 14 seconds, we can use the formula ω = Δθ/Δt, where Δθ is the change in angle and Δt is the change in time. In this case, Δθ = 1 radian and Δt = 14 seconds. Therefore, the radius of the circular motion is r = ω^2r/Δθ = (1 radian/sec)^2 * r/1 radian = r.

Now, we can calculate the centripetal force using the given mass of 35kg and the angular speed of 1 radian/sec: F = (35kg)(1 radian/sec)^2 * r = 35r N.

Next, we need to find the new angular speed when the ride starts to brake. Since the angular speed becomes half, the new angular speed is 1/2 radian/sec.

To find the number of complete rotations in 2.25 minutes, we can use the formula T = 2π/ω, where T is the period (time for one complete rotation) and ω is the angular speed. In this case, T = 2.25 minutes = 2.25 * 60 seconds = 135 seconds. Therefore, the number of complete rotations is N = T/2π * ω = 135 seconds/2π * (1/2 radian/sec) = 135/4π rotations.

In conclusion, the ride will make approximately 135/4π rotations in 2.25 minutes if the angular speed remains constant until it starts to brake.