Question: A torque of 10 Nm is applied to a wheel with a moment of inertia of 5 kg·m². What is the angular acceleration of the wheel?
Options:
2 rad/s²
5 rad/s²
10 rad/s²
20 rad/s²
Correct Answer: 2 rad/s²
Solution:
Using τ = Iα, we have α = τ/I = 10 Nm / 5 kg·m² = 2 rad/s².
A torque of 10 Nm is applied to a wheel with a moment of inertia of 5 kg·m². Wha
Practice Questions
Q1
A torque of 10 Nm is applied to a wheel with a moment of inertia of 5 kg·m². What is the angular acceleration of the wheel?
2 rad/s²
5 rad/s²
10 rad/s²
20 rad/s²
Questions & Step-by-Step Solutions
A torque of 10 Nm is applied to a wheel with a moment of inertia of 5 kg·m². What is the angular acceleration of the wheel?
Step 1: Understand the formula for angular acceleration, which is α = τ / I.
Step 2: Identify the values given in the question: torque (τ) is 10 Nm and moment of inertia (I) is 5 kg·m².
Step 3: Substitute the values into the formula: α = 10 Nm / 5 kg·m².
Step 4: Perform the division: 10 divided by 5 equals 2.
Step 5: Conclude that the angular acceleration (α) of the wheel is 2 rad/s².
Torque and Angular Acceleration – This question tests the relationship between torque (τ), moment of inertia (I), and angular acceleration (α) using the formula τ = Iα.
Units of Measurement – It assesses the understanding of units involved in rotational dynamics, specifically Newton-meters for torque and kg·m² for moment of inertia.
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