Question

A particle makes 240 revolution per minute on a circle of radius 2m. What is its period, period, angular velocity, linear velocity, and acceleration?

Answer 1

To solve this problem, we can use the following formulas:

1. Period (T) = 1 / Frequency (f)
2. Angular velocity (ω) = 2π * Frequency (f)
3. Linear velocity (v) = ω * Radius (r)
4. Centripetal acceleration (a) = ω^2 * Radius (r)

Given:

• The particle makes 240 revolutions per minute.
• The radius of the circle is 2 meters.

Let's calculate the values step by step:

1. Period (T) = 1 / Frequency (f)

The frequency (f) can be obtained by converting the number of revolutions per minute to revolutions per second: f = 240 rev/min * (1 min/60 s) = 4 rev/s

Now, calculate the period: T = 1 / f = 1 / 4 = 0.25 seconds

So, the period of the particle is 0.25 seconds.

2. Angular velocity (ω) = 2π * Frequency (f)

Using the value of frequency from above: ω = 2π * f = 2π * 4 = 8π rad/s

Therefore, the angular velocity of the particle is 8π rad/s.

3. Linear velocity (v) = ω * Radius (r)

Using the given radius of 2 meters and the angular velocity: v = ω * r = 8π * 2 = 16π m/s

Hence, the linear velocity of the particle is 16π m/s.

4. Centripetal acceleration (a) = ω^2 * Radius (r)

Using the angular velocity and radius: a = ω^2 * r = (8π)^2 * 2 = 64π^2 m/s²

Thus, the centripetal acceleration of the particle is 64π^2 m/s².