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 [tex]T=0. 5s[/tex] and since the frequency [tex]f[/tex] is the inverse of the period, we have:
[tex]f=\frac{1}{T}=\frac{1}{0.5 s}[/tex]
[tex]f=2 Hz[/tex]
b-the distance it travels around the circular path
Here we have to calculate the perimeter [tex]P[/tex] of the circular path:
[tex]P=\pi D[/tex]
Where [tex]D=45 cm=0.45 m[/tex] is the diameter
[tex]P=\pi (0.45 m)=1.413 m[/tex]
c-linear velocity
We can calculate the linear velocity [tex]V[/tex] by:
[tex]V=\frac{P}{T}=\frac{1.413 m}{0.5 s}[/tex]
[tex]V=2.82 m/s[/tex]
d-angular velocity
Angular velocity [tex]\omega[/tex] is given by:
[tex]\omega=2 \pi f[/tex]
[tex]\omega=2 \pi (2 Hz)[/tex]
[tex]\omega=12.56 rad/s[/tex]
e-centripetal acceleration
Centripetal acceleration [tex]a_{c}[/tex] is given by:
[tex]a_{c}=\frac{V^{2}}{r}[/tex]
[tex]a_{c}=\frac{(2.82 m/s)^{2}}{0.225 m}[/tex]
[tex]a_{c}=35.34 m/s^{2}[/tex]
