A carnival ride has a radius of 2.18 m and rotates once every 0.82 sec. What would the speed of a rider be that has been flung from the ride? What would be the angular speed of a second rider who remains on the ride?
To find the speed of a rider who has been flung from the ride, we can use the formula for linear velocity:
Linear velocity (v) = angular velocity (ω) × radius (r)
First, we need to find the angular velocity of the ride. The angular velocity (ω) is the rate at which the ride rotates and is given by:
ω = 2π / T
where T is the period of rotation. In this case, the period T is 0.82 seconds.
ω = 2π / 0.82 ≈ 7.68 rad/s
Now, we can calculate the linear velocity of a rider flung from the ride. The rider will move in a straight line tangent to the circular path. Using the given radius (r) of 2.18 m, we can substitute the values into the formula:
v = ω × r
v = 7.68 rad/s × 2.18 m ≈ 16.74 m/s
Therefore, the speed of a rider who has been flung from the ride would be approximately 16.74 m/s.
To find the angular speed of a second rider who remains on the ride, we already have the value for angular velocity (ω) of the ride, which is 7.68 rad/s. The angular speed of any object on the ride would be equal to the angular velocity of the ride itself.
Therefore, the angular speed of the second rider who remains on the ride would also be 7.68 rad/s.