Question

a bicycle tire starts from rest and has an angular acceleration of 0.23 rad/s2. when it has made 10.0 rev, what is its kinetic energy? assume the moment of inertia is 0.18 kg m2.

Answer 1

The kinetic energy of the bicycle tire can be calculated using the formula KErot = 0.5 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. To find ω, we can use the equation ω^2 = ω0^2 + 2αθ, where ω0 is the initial angular velocity, α is the angular acceleration, and θ is the number of revolutions.

Step-by-step explanation:

To calculate the kinetic energy of the bicycle tire, we can make use of the formula:

KErot = 0.5 * I * ω^2

Where KErot is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.

Given that the bicycle tire starts from rest and has an angular acceleration of 0.23 rad/s^2 and has made 10.0 revolutions, we need to calculate the final angular velocity using the equation:

ω^2 = ω0^2 + 2αθ

Where ω0 is the initial angular velocity, α is the angular acceleration, and θ is the number of revolutions.

Once we have the final angular velocity, we can substitute it into the first equation to find the kinetic energy.

KErot = 0.5 * I * ω^2

Answer 2

To calculate the kinetic energy of a rotating bicycle tire, use the formula KE = 0.5 * I * ω², where I is the moment of inertia and ω is the angular velocity. The angular velocity can be found using the formula ω = √(2 * α * θ), where α is the angular acceleration and θ is the angle covered. Then, substitute the values into the formula to find the kinetic energy.

Step-by-step explanation:

To calculate the kinetic energy of the rotating bicycle tire, we can use the formula KE = 0.5 * I * ω², where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity. Given that the bicycle tire starts from rest and has an angular acceleration of 0.23 rad/s², we can find its angular velocity using the formula ω = √(2 * α * θ), where α is the angular acceleration and θ is the angle covered. In this case, the angle covered is 10.0 revolutions, which is equal to 20π radians. Thus, ω = √(2 * 0.23 * 20π) rad/s. Once we have the angular velocity, we can then calculate the kinetic energy using the formula KE = 0.5 * I * ω². Substituting the given moment of inertia of 0.18 kg m², we can find the kinetic energy of the rotating bicycle tire.