Question Detail

PHY 101 Rigid Body Dynamics Objective Question
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Question

For a given angular speed, why can a thin rod rotating about an axis through one end be considered more 'destructive' or effective than the same rod rotating about an axis through its center?
Options
A Because its angular velocity is higher.
B Because its moment of inertia is larger, requiring a greater torque for the same angular acceleration.
Correct Answer
C Because its mass is more concentrated at the center.
D Because its angular momentum is smaller.
Correct Answer

Option B is the correct answer.

Detailed Explanation

For a given angular speed ω, the rotational kinetic energy is ½ I ω² and the angular momentum is I ω. A rod rotating about its end has a larger moment of inertia (I_end = ⅓ M L²) than about its center (I_cm = 1/12 M L²). A larger I means greater rotational kinetic energy and angular momentum for the same ω. The statement about 'destructiveness' relates to the greater torque (τ = I α) needed to stop it or the greater energy it possesses, both stemming from the larger moment of inertia.

Hint

Consider how the moment of inertia differs for these two axes and its effect on rotational quantities like energy and angular momentum for a fixed angular speed.

Question Info

Course: PHY 101
Topic: Rigid Body Dynamics
Type: Objective
Difficulty: Not specified
Question 654 of 1250
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