# Rotational inertia of truck and trailer

• CH_GR
In summary, to compute the energy required to accelerate a truck and trailer from 0 to 60 mph, the moment of inertia of the wheels should be considered. The wheels can be approximated as a combination of the tire and rim, with an inertia of 0.8 times the static mass. This applies to all passenger car and truck tires. The kinetic energy of a wheel is (2/5) times the mass times the velocity squared, and for 18 wheels this is added to the total kinetic energy of the vehicle. The weight of the wheels (mg) can vary, with steel rims weighing 200 lbs and aluminum rims weighing 170 lbs.

#### CH_GR

I need to compute the energy to get a truck and trailer from 0 to 60 mph from rest taking into account the mass of truck and trailer and inertia of wheels and rims.

Do I treat the rims and tires as a cylindrical shell or solid cylinder? Once I find the energy of the tires and rims do I just add that to the 1/2MV^2 for truck and trailer?

thanks.

The moment of inertia of a cylindrical shell is mR2, while the solid cylinder is (1/2)mR2. The wheels are about 0.8mR2. For an automobile, the rolling tires add about 4% to the dynamic mass e.g., kinetic energy KE = (1/2)(1.04) mv2, where m is the static mass.

By wheel you mean tire and rim? Then I could use 0.8MR^2 to approximate the inertia instead of treating it separately as cylindrical shell and solid shell?

Does this approximation apply to all passenger car and truck tires?

thanks.

Yes, the tire and rim together are about I = 0.8 mR2. The 18 tires plus rims (=wheels) are only a small percentage (<5%) of total truck & trailer mass.
So the kinetic energy of a wheel is
KE = (1/2) I w2 = (1/2)(0.8)m (Rw)2 = (2/5) mv2 (rotational energy only)
For 18 wheels it is
KE = (36/5)mv2
This gets added to the total vehicle kinetic energy:
kE tot = (1/2)Mv2 + (36/5) mv2
How much do the wheels weigh (mg)? 200 pounds?

The wheels weigh 200 lbs for steel rims and 170 lbs for aluminum rims.

Thanks for the info.

## 1. What is rotational inertia of a truck and trailer?

The rotational inertia of a truck and trailer is a measure of their resistance to changes in rotational motion. It is also known as moment of inertia and depends on the mass and distribution of mass in the truck and trailer.

## 2. How is rotational inertia of a truck and trailer calculated?

The rotational inertia of a truck and trailer can be calculated using the formula I = MR², where I is the moment of inertia, M is the mass, and R is the distance from the axis of rotation to the mass. This formula can be applied to each individual part of the truck and trailer and then added together to find the total rotational inertia.

## 3. What factors affect the rotational inertia of a truck and trailer?

The rotational inertia of a truck and trailer is affected by the mass and distribution of mass in each individual part. The farther the mass is from the axis of rotation, the higher the rotational inertia will be. Additionally, the shape and size of the truck and trailer can also affect its rotational inertia.

## 4. Why is rotational inertia important for trucks and trailers?

Understanding the rotational inertia of a truck and trailer is important for designing and operating them safely. It can also affect their handling and stability on the road. A higher rotational inertia can make it more difficult to turn or stop the truck and trailer, while a lower rotational inertia can make it easier to maneuver.

## 5. How can the rotational inertia of a truck and trailer be changed?

The rotational inertia of a truck and trailer can be changed by altering the mass or distribution of mass in each individual part. This can be done by adding or removing weight, changing the shape or size of the parts, or adjusting the position of the mass relative to the axis of rotation. These changes can affect the overall handling and performance of the truck and trailer.