# What is the total rotational kinetic energy of the wheels?

• brncsfns5621
In summary, the total rotational kinetic energy of the two wheels of a moped, with a rider of mass 50kg traveling at a speed of 20 m/s, is 8 Joules. The formula used to calculate this energy is KEr = 1/2Iw^2, where I represents moment of inertia and w represents angular velocity. The conversion between linear speed and angular speed is v = wr, and 1 degree is equal to \frac{\pi}{180} radians.
brncsfns5621
A 50kg rider on a moped of mass 75kg is traveling with a speed of 20 m/s. Each of the two wheels of the moped has a radius of 0.2m and a moment of inertia of 0.2 kg*m^2. What is the total rotational kinetic energy of teh wheels?

KEr = 1/2Iw^2
= 1/2(.02)(20)^2
= 4
Two wheels = 2 *4 = 8 Joules

I think I am wrong as the angular velocity (w) has to be in rad/s. For some reason, I can not figure out how to get that. What is the formula for w?

Yes, that formula requires angular speed, not linear speed. They are related by: v = wr.

(A complete circle, one circumference, is equivalent to $2 \pi$ radians.)

Yeah, you're using an incorrect value for $\omega$.

If you're confused by the radians, it might be helpful to figure out how many degrees per second the wheels are turning, and then use the conversion:
$$1 \rm{degree}=\frac{\pi}{180} \rm{radians}$$

thanks. I knew I was forgetting something. It just didn't look right.

## 1. What is rotational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation around an axis. It is a type of kinetic energy that depends on the mass, shape, and speed of the rotating object.

## 2. How do you calculate rotational kinetic energy?

The formula for calculating rotational kinetic energy is K = 1/2 * I * ω², where K is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity of the rotating object. The units for rotational kinetic energy are Joules (J).

## 3. What is the moment of inertia?

Moment of inertia is a measure of an object's resistance to change its rotation. It depends on the mass, shape, and distribution of mass of the object. The larger the moment of inertia, the more rotational kinetic energy an object will have for a given angular velocity.

## 4. How does the total rotational kinetic energy of wheels affect vehicle performance?

The total rotational kinetic energy of the wheels affects vehicle performance by determining how much energy is needed to accelerate or decelerate the wheels. This can impact the speed and handling of the vehicle, as well as its fuel efficiency.

## 5. Can the total rotational kinetic energy of the wheels be changed?

Yes, the total rotational kinetic energy of the wheels can be changed by altering the mass, shape, or speed of the rotating wheels. This can be done through modifications to the vehicle's design or by changing the driving habits of the operator.

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