Question

Un carro de juguete da vueltas en una pista circular de 45 cm de diametro si emplea 0,5 s en realizar una vuelta dteemina

Answer 1

Answers:

The complete question in english is written below:

A toy car spins on a circular track 45 cm in diameter. If it uses 0.5 seconds to make a complete circle, determine:

a- period and frequency in one circle

b-the distance it travels around the circular path

c-linear velocity

d-angular velocity

e-centripetal acceleration

a- period and frequency in one circle

According to the given information the period is $T=0. 5s$ and since the frequency $f$ is the inverse of the period, we have:

$f=\frac{1}{T}=\frac{1}{0.5 s}$

$f=2 Hz$

b-the distance it travels around the circular path

Here we have to calculate the perimeter $P$ of the circular path:

$P=\pi D$

Where $D=45 cm=0.45 m$ is the diameter

$P=\pi (0.45 m)=1.413 m$

c-linear velocity

We can calculate the linear velocity $V$ by:

$V=\frac{P}{T}=\frac{1.413 m}{0.5 s}$

$V=2.82 m/s$

d-angular velocity

Angular velocity $\omega$ is given by:

$\omega=2 \pi f$

$\omega=2 \pi (2 Hz)$

$\omega=12.56 rad/s$

e-centripetal acceleration

Centripetal acceleration $a_{c}$ is given by:

$a_{c}=\frac{V^{2}}{r}$

$a_{c}=\frac{(2.82 m/s)^{2}}{0.225 m}$

$a_{c}=35.34 m/s^{2}$