To find the linear velocity and acceleration of a particle moving in a circle, we need to use the following formulas:
Linear velocity (v) = 2πr/T Centripetal acceleration (a) = v^2 / r
Where: r is the radius of the circle, T is the period or time taken for one revolution (in this case, 1 minute or 60 seconds), π is a mathematical constant approximately equal to 3.14159.
Given: Radius (r) = 2m Revolutions per minute = 240
First, let's calculate the period (T) in seconds: T = 60 seconds / 240 revolutions = 0.25 seconds/revolution
Next, we can calculate the linear velocity (v): v = 2πr / T v = 2 * 3.14159 * 2 / 0.25 v ≈ 50.26548 m/s
Finally, we can calculate the centripetal acceleration (a): a = v^2 / r a = (50.26548)^2 / 2 a ≈ 1261.62 m/s^2
Therefore, the linear velocity of the particle is approximately 50.27 m/s, and the centripetal acceleration is approximately 1261.62 m/s^2.