A car with a total mass of 1.48 103 kg has wheels of radius 33.5 cm and moment of inertia 0.810 kg · m2.

(a) Find the car's translational kinetic energy when the car is moving at a speed of 30.0 m/s.
(b) Find the car's rotational energy when the car is moving at a speed of 30.0 m/s.

To find the car's translational kinetic energy, we can use the equation:

Kinetic energy = 1/2 * mass * velocity^2

Step 1: Convert the radius of the wheels from cm to meters:
Radius = 33.5 cm * (1m / 100 cm) = 0.335 m

(a) Translational Kinetic Energy:
Step 2: Calculate the mass of each wheel:
Mass of each wheel = Total mass of the car / Number of wheels
Mass of each wheel = 1.48 x 10^3 kg / 4 wheels = 370 kg

Step 3: Calculate the moment of inertia of each wheel:
Moment of inertia of each wheel = 1/2 * mass of each wheel * radius^2
Moment of inertia of each wheel = 1/2 * 370 kg * (0.335 m)^2 = 20.775 kg · m^2

Step 4: Calculate the total rotational kinetic energy of all the wheels combined:
Rotational kinetic energy = 1/2 * moment of inertia of each wheel * (angular velocity)^2
The car is moving in a straight line, so the angular velocity is 0:
Rotational kinetic energy = 1/2 * 20.775 kg · m^2 * (0)^2 = 0 joules

Step 5: Calculate the translational kinetic energy of the car:
Translational kinetic energy = 1/2 * total mass * velocity^2
Translational kinetic energy = 1/2 * 1.48 x 10^3 kg * (30 m/s)^2 = 666600 joules

Therefore, the car's translational kinetic energy when moving at a speed of 30.0 m/s is 666600 joules.

(b) Rotational Kinetic Energy:
The car's rotational kinetic energy when it is moving in a straight line is 0 joules because the angular velocity is 0 (the wheels do not rotate).