Question

A ball is spun around in circular motion such that it completes 50 rotations in 25 s. What is the frequency of its rotation? 2. A runner completes 5 laps around a circular track in 450 s. What is the frequency? 3. A pendulum completes one cycle in 15 s. What is the frequency? 4. An object is spun around in circular motion such that its frequency is 12 Hz. How much time will be required to complete 48 rotations?

Answer 1

Answer:

1. $f = 2 Hz$

2. $f = 0.011 Hz$

3. $f = 0.067 Hz$

4. $t = 4 s$

Explanation:

1. The frequency of rotation is given by:

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

Where:

ω: is the angular speed = 50 rotations (revolutions) in 25 s.

We need to convert the units of ω.

$\omega = \frac{50 rev}{25 s}*\frac{2\pi rad}{1 rev} = 4\pi rad/s$

Now, the frequency is:

$f = \frac{4\pi rad/s}{2\pi} = 2 Hz$

2. The frequency is:

We know:

5 laps = 5 revolutions

t: time = 450 s

$f = \frac{\omega}{2\pi} = \frac{\frac{5 rev}{450 s}*\frac{2\pi rad}{1 rev}}{2\pi} = 0.011 Hz$    

3. The frequency of the pendulum is:

$f = \frac{\omega}{2\pi} = \frac{\frac{1 rev}{15 s}*\frac{2\pi rad}{1 rev}}{2\pi} = 0.067 Hz$

4. We have:

θ: number of revolutions = 48 rev

f = 12 Hz

t =?

The time can be calculated as follows:

$f = \frac{\omega}{2\pi} = \frac{\theta}{2\pi t}$

$t = \frac{\theta}{2\pi f} = \frac{48 rev*\frac{2\pi rad}{1 rev}}{2\pi*12 Hz} = 4 s$

I hope it helps you!