Two objects of equal mass are on a turning wheel. Mass 1 is located at the rim of the wheel while mass 2 is located halfway between the rim and the axis of rotation. The wheel is rotating with a non-zero angular acceleration. For each of the following statements select the correct option to complete the statement.

The tangential acceleration of mass 1 is______________the tangential acceleration of mass 2. (equal to?)

The centripetal (radial) acceleration of mass 1 is______________the centripetal acceleration of mass 2. (greater than?)

For a given time, the angle covered by mass 2 is______________the angle covered by mass 1. (equal to?)

The magnitude of the total acceleration of mass 1 is_____________the total acceleration of mass 2. (greater than?)

The moment of inertia of mass 1 about the axis of rotation is_____________the moment of inertia of mass 2 about the axis of rotation . (greater than?)

For a given time, mass 1 travels a distance that is____________the distance traveled by mass 2. (greater than?)

The speed of mass 1 is____________the speed of mass 2. (greater than?)

The angular acceleration of mass 2 is________________the angular acceleration of mass 1. (equal to?)

greater than

To answer each statement, we need to understand the concepts of tangential acceleration, centripetal (radial) acceleration, angle covered, total acceleration, moment of inertia, distance traveled, speed, and angular acceleration. Let's break down each statement one by one:

1. The tangential acceleration of mass 1 is ____________ the tangential acceleration of mass 2.

To determine the tangential acceleration, we use the formula a_t = r * α, where a_t represents the tangential acceleration, r is the radius, and α is the angular acceleration.

Since both masses are on the same turning wheel and have the same angular acceleration, their tangential acceleration will be equal. Therefore, the correct option is "equal to."

2. The centripetal (radial) acceleration of mass 1 is ____________ the centripetal acceleration of mass 2.

To calculate the centripetal acceleration, we use the formula a_c = r * ω^2, where a_c represents the centripetal acceleration, r is the radius, and ω is the angular velocity.

Since both masses are on the same turning wheel and have the same radius, their centripetal acceleration will be equal. Therefore, the correct option is "equal to."

3. For a given time, the angle covered by mass 2 is ____________ the angle covered by mass 1.

Since mass 2 is located halfway between the rim and the axis of rotation, it will need to travel a smaller radius in order to cover the same angle as mass 1. Therefore, the correct option is "equal to."

4. The magnitude of the total acceleration of mass 1 is ____________ the total acceleration of mass 2.

The total acceleration is the vector sum of the tangential acceleration and the centripetal acceleration. Since both masses have the same tangential and centripetal accelerations, their total accelerations will also be equal. Therefore, the correct option is "equal to."

5. The moment of inertia of mass 1 about the axis of rotation is ____________ the moment of inertia of mass 2 about the axis of rotation.

The moment of inertia depends on the mass distribution relative to the axis of rotation. Since mass 1 is located at the rim of the wheel (farther from the axis of rotation) and mass 2 is halfway between the rim and the axis of rotation, mass 1 will have a greater moment of inertia compared to mass 2. Therefore, the correct option is "greater than."

6. For a given time, mass 1 travels a distance that is ____________ the distance traveled by mass 2.

Since mass 1 is located at the rim of the wheel (farther from the axis of rotation), it will travel a larger circumference compared to mass 2. Therefore, the correct option is "greater than."

7. The speed of mass 1 is ____________ the speed of mass 2.

Since they are on the same turning wheel and have the same angular velocity, the linear velocity at any point on the wheel will be directly proportional to the distance from the axis of rotation. Thus, mass 1, located at the rim, will have a greater linear velocity compared to mass 2, located halfway between the rim and the axis of rotation. Therefore, the correct option is "greater than."

8. The angular acceleration of mass 2 is ____________ the angular acceleration of mass 1.

According to the problem statement, the wheel is rotating with a non-zero angular acceleration. Since both masses are on the same wheel, they will have the same angular acceleration. Therefore, the correct option is "equal to."