Answer:
Explanation:
Given that,
Radius of the wheel, r = 20 cm = 0.2 m
Initial speed of the wheel, [tex]\omega_i=120\ rpm=753.98\ rad/s[/tex]
Displacement, [tex]\theta=90\ rev=565.48\ rad[/tex]
To find,
The angular acceleration and the distance covered by the car.
Solution,
Let [tex]\alpha[/tex] is the angular acceleration of the car. Using equation of rotational kinematics as :
[tex]\theta=\omega_i t+\dfrac{1}{2}\alpha t^2[/tex]
[tex]565.48=753.98\times 60+\dfrac{1}{2}\alpha (60)^2[/tex]
[tex]\alpha =-24.81\ rad/s^2[/tex]
Let t is the time taken by the car before coming to rest.
[tex]t=\dfrac{\omega_f-\omega_i}{\alpha }[/tex]
[tex]t=\dfrac{0-753.98}{-24.81}[/tex]
t = 30.39 seconds
Let v is the linear velocity of the car. So,
[tex]v=r\times \omega_i[/tex]
[tex]v=0.2\times 753.98[/tex]
v = 150.79 m/s
Let d is the distance covered by the car. It can be calculated as :
[tex]d=v\times t[/tex]
[tex]d=150.79\ m/s\times 30.39\ s[/tex]
d = 4582.5 meters
or
d = 4.58 km
