Answer to Question #116770 in Mechanics | Relativity for Siya

Question

An experimental flywheel, used to store energy and replace a motor vehicle engine, is a solid disk of mass 200kg and radius 0,40m
a)What is the flywheel's rotational inertia?
b)when driving at 22,4m/s the fully energized flywheel is rotating at an angular speed of 3160 rad/s. What is the initial rotational kinetic energy of the flywheel?
c)If the total mass of the car is 1000kg find the ratio of the initial rotational kinetic energy of the flywheel to translational kinetic energy of the car.
d)If the force of air resistance on the car is 670N how far can the car travel at a speed of 22,4m/s with the initial stored energy?(Ignore losses of mechanical energy due to means other than air resistance)

Answer 1

a)

$$I=0.5mr^2=0.5(200)(0.4)^2=16\ kg\cdot m^2$$

b)

$$K_{rot,i}=0.5I\omega_i^2=0.5(16)(3160)^2=7.99\cdot 10^7\ J$$

c)

$$\frac{K_{rot,i}}{K_{t}}=\frac{0.5(16)(3160)^2}{0.5(1000)(22.4)^2}=318$$

d)

$$K_t+K_{rot,i}=F_rs$$

$$0.5(16)(3160)^2+0.5(1000)(22.4)^2=670s$$

$$s=120000\ m=120\ km$$