Question

A bicycle wheel spins with an angular momentum of LL = 5.0 kg⋅m²/s. If the wheel has mass mmm = 2.4 kg and radius r = 0.38 m, how long does it take the wheel to make 1 full rotation?

Answer 1

To calculate the time for one full rotation of the bicycle wheel, we need to find the angular velocity using its angular momentum. This can be done by calculating the moment of inertia and substituting it in the formula. Finally, the time can be determined using the angular velocity.

Step-by-step explanation:

To calculate the time it takes for the bicycle wheel to make one full rotation, we need to find the angular velocity of the wheel. Angular velocity is the rate at which an object rotates and is measured in radians per second (rad/s). We can use the formula:

angular velocity = angular momentum/moment of inertia

Given that the angular momentum (L) is 5.0 kg⋅m²/s and the moment of inertia (I) of the wheel can be calculated using the formula:

moment of inertia = 0.5 * mass * radius²

Substituting the given values, we can solve for the moment of inertia and then use it to find the angular velocity. Finally, we can use the formula:

time = 2π / angular velocity

Substituting the calculated angular velocity, we can determine the time it takes for the wheel to make one full rotation.