Question

Two identical masses are connected to two different flywheels that are initially stationary. Flywheel A is larger and has more mass, but has hexagonal sections where material has been removed. The attached masses are released from rest and allowed to fall a height h.Which of the following statements about their angular accelerations is true? a. The angular acceleration of the two flywheels is different but it is impossible to tell which is greater. b. The angular acceleration of flywheel A is greater The angular acceleration of flywheel B is greater. c. Not enough information is provided to determine. d. The angular accelerations of the two flywheels are equal.

Answer 1

Answer:

a) True. There is dependence on the radius and moment of inertia, no data is given to calculate the moment of inertia

c) True. Information is missing to perform the calculation

Explanation:

Let's consider solving this exercise before seeing the final statements.

We use Newton's second law Rotational

      τ = I α

     T r = I α

     T gR = I α

     Alf = T R / I (1)

     T = α I / R

Now let's use Newton's second law in the mass that descends

     W- T = m a

     a = (m g -T) / m

The two accelerations need related

     a = R α

    α = a / R

    a = (m g - α I / R) / m

    R α = g - α I /m R

    α (R + I / mR) = g

    α = g / R (1 + I / mR²)

We can see that the angular acceleration depends on the radius and the moments of inertia of the steering wheels, the mass is constant

Let's review the claims

a) True. There is dependence on the radius and moment of inertia, no data is given to calculate the moment of inertia

b) False. Missing data for calculation

c) True. Information is missing to perform the calculation

d) False. There is a dependency if the radius and moment of inertia increases angular acceleration decreases