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sasho
7 days ago
13

On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are unifo

rmly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s. What is the tangential acceleration of the passengers during the first 21 s of the ride answer
Physics
1 answer:
Yuliya22 [1.1K]7 days ago
3 0

Answer:

a = 0.5 m/s²

Explanation:

Using the concept of angular acceleration as a change over time, and considering that the seats start from a stationary position, we can derive the angular acceleration as follows:

ωf = ω₀ + α*t

⇒ ωf = α*t ⇒ α = \frac{wf}{t} = \frac{1.4 rad/s}{21 s} = 0.067 rad/s2

The relationship between linear speed and angular velocity is given by:

v = ω*r

By applying the definition of linear acceleration (which in this situation is tangential acceleration) alongside angular acceleration, we establish a corresponding link between tangential and angular accelerations, as shown:

a = α*r⇒ a = 0.067 rad/sec²*7.5 m = 0.5 m/s²

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