Question

In the following illustration, a force of 100 N rolls the solid cylinder for 4 s. The cylinder starts from rest and does not change shape. The angular velocity of the cylinder is most nearly:

a. 5 rad/s
b. 10 rad/s
c. 20 rad/s
d. Need more data

Answer 1

To determine the angular velocity of a cylinder after a force is applied, additional data such as torque, moment of inertia, or angular acceleration is required. With only the force value and time duration, the correct answer to the student's question is 'Need more data'.

The correct option is d.

Step-by-step explanation:

To calculate the angular velocity after applying a force on a solid cylinder, we need to know either the torque applied, the moment of inertia of the cylinder, or the angular acceleration. Since this information is not given in the question, we cannot determine the angular velocity just from the force value and time duration. Therefore, the correct answer is d. Need more data.

Clarification about provided scenarios

• The scenario with the particle colliding with the cylinder refers to the conservation of angular momentum and doesn't directly give us the needed values for the initial scenario.
• The object with a given angular acceleration can help us find the final angular velocity if the initial angular velocity and time are known, as in example 20.
• Using the work energy theorem to calculate angular velocity with a known force, distance, and moment of inertia as in example 125 is possible, but again, that's not the case in the initial scenario.
• The bicycle wheel example demonstrates calculating angular acceleration, but it also depends on the known final angular velocity and time, not applicable in the initial scenario.

In summary, we cannot compute the angular velocity without additional data relating force to the rotational effect on the cylinder (such as torque or angular acceleration).

The correct option is d.