A torque τ is applied to a rigid body with moment of inertia I. If the body star
Practice Questions
Q1
A torque τ is applied to a rigid body with moment of inertia I. If the body starts from rest, what is the angular displacement θ after time t?
(1/2)(τ/I)t^2
(τ/I)t^2
(1/2)(I/τ)t^2
(I/τ)t^2
Questions & Step-by-Step Solutions
A torque τ is applied to a rigid body with moment of inertia I. If the body starts from rest, what is the angular displacement θ after time t?
Step 1: Understand that torque (τ) is a force that causes rotation.
Step 2: Know that moment of inertia (I) is a measure of how difficult it is to change the rotation of the body.
Step 3: Recognize that when a torque is applied, it causes an angular acceleration (α).
Step 4: Use the formula for angular acceleration: α = τ/I.
Step 5: Since the body starts from rest, the initial angular velocity is 0.
Step 6: Use the equation of motion for rotation: θ = (1/2)αt^2.
Step 7: Substitute α with τ/I in the equation: θ = (1/2)(τ/I)t^2.
Step 8: This gives you the angular displacement θ after time t.
Torque and Moment of Inertia – Understanding the relationship between torque, moment of inertia, and angular acceleration in rotational motion.
Equations of Motion for Rotation – Applying the equations of motion specifically for rotational dynamics, similar to linear motion but adapted for angular quantities.
