Question

Particle moves in a circle of radius 90m with a constant speed 25m/s. how many revolution does it make in 30sec​

Answer 1

Answer:

n =1.33 revolutions

Explanation:

Uniform Circular Motion

The angular speed can be calculated in two different ways:

$\displaystyle \omega=\frac{v}{r}$

Where:

v = tangential speed

r = radius of the circle described by the rotating object

Also:

$\omega=2\pi f$

Where:

f = frequency

Solving for f:

$\displaystyle f=\frac{\omega}{2\pi}$

Since the frequency is calculated when the number of revolutions n and the time t are known:

$\displaystyle f=\frac{n}{t}$

We can solve for n:

n=f.t

The particle moves in a circle of r=90 m with a speed v=25 m/s. Thus the angular speed is:

$\displaystyle \omega=\frac{25}{90}$

$\displaystyle \omega=0.278\ rad/s$

Now we calculate f:

$\displaystyle f=\frac{0.278}{2\pi}$

$f=0.04421\ Hz$

Calculating the number of revolutions:

n = 0.04421*30

n =1.33 revolutions