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.
To complete the statements, we need to understand the relationship between the location of an object on a rotating wheel and its angular acceleration. Here are the options to choose from:
A) The magnitudes of the linear accelerations of both objects are the same.
B) The magnitudes of the linear accelerations of both objects are different.
C) The angular accelerations of both objects are the same.
D) The angular accelerations of both objects are different.
To determine the correct options, we can use the concept of rotational kinematics. The linear acceleration of an object on a rotating wheel depends on the distance of the object from the axis of rotation.
Statement 1: Mass 1 at the rim of the wheel.
Since Mass 1 is located at the rim of the wheel, it has the largest distance from the axis of rotation. The linear acceleration of an object on a rotating wheel is directly proportional to its distance from the axis of rotation. Therefore, Mass 1 will experience a greater linear acceleration.
The correct option is B) The magnitudes of the linear accelerations of both objects are different.
Statement 2: Mass 2 is located halfway between the rim and the axis of rotation.
Mass 2 is located at a distance between the rim and the axis of rotation, which is closer to the axis compared to Mass 1. As a result, Mass 2 will experience a smaller linear acceleration compared to Mass 1.
The correct option is B) The magnitudes of the linear accelerations of both objects are different.
Statement 3: The wheel is rotating with a non-zero angular acceleration.
The angular acceleration of an object on a rotating wheel is the same for all objects on the wheel. This is because they all rotate together as a rigid body. Therefore, both Mass 1 and Mass 2 will have the same angular acceleration.
The correct option is C) The angular accelerations of both objects are the same.
In summary:
1) The magnitudes of the linear accelerations of both objects are different.
2) The magnitudes of the linear accelerations of both objects are different.
3) The angular accelerations of both objects are the same.