Answer:
1. [tex] f = 2 Hz [/tex]
2. [tex] f = 0.011 Hz [/tex]
3. [tex] f = 0.067 Hz [/tex]
4. [tex] t = 4 s [/tex]
Explanation:
1. The frequency of rotation is given by:
[tex] f = \frac{\omega}{2\pi} [/tex]
Where:
ω: is the angular speed = 50 rotations (revolutions) in 25 s.
We need to convert the units of ω.
[tex] \omega = \frac{50 rev}{25 s}*\frac{2\pi rad}{1 rev} = 4\pi rad/s [/tex]
Now, the frequency is:
[tex] f = \frac{4\pi rad/s}{2\pi} = 2 Hz [/tex]
2. The frequency is:
We know:
5 laps = 5 revolutions
t: time = 450 s
[tex] f = \frac{\omega}{2\pi} = \frac{\frac{5 rev}{450 s}*\frac{2\pi rad}{1 rev}}{2\pi} = 0.011 Hz [/tex]
3. The frequency of the pendulum is:
[tex]f = \frac{\omega}{2\pi} = \frac{\frac{1 rev}{15 s}*\frac{2\pi rad}{1 rev}}{2\pi} = 0.067 Hz[/tex]
4. We have:
θ: number of revolutions = 48 rev
f = 12 Hz
t =?
The time can be calculated as follows:
[tex] f = \frac{\omega}{2\pi} = \frac{\theta}{2\pi t} [/tex]
[tex] t = \frac{\theta}{2\pi f} = \frac{48 rev*\frac{2\pi rad}{1 rev}}{2\pi*12 Hz} = 4 s [/tex]
I hope it helps you!
