A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2
Practice Questions
Q1
A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2 rad/s², what will be its angular velocity after 5 seconds? (2023)
20 rad/s
10 rad/s
15 rad/s
25 rad/s
Questions & Step-by-Step Solutions
A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2 rad/s², what will be its angular velocity after 5 seconds? (2023)
Step 1: Identify the initial angular velocity (ω₀). In this case, it is 10 rad/s.
Step 2: Identify the angular acceleration (α). Here, it is 2 rad/s².
Step 3: Identify the time (t) for which the wheel accelerates. In this case, it is 5 seconds.
Step 4: Use the formula for angular velocity: ω = ω₀ + αt.
Step 5: Substitute the values into the formula: ω = 10 rad/s + (2 rad/s² * 5 s).
Step 6: Calculate the product of angular acceleration and time: 2 rad/s² * 5 s = 10 rad/s.
Step 7: Add the result to the initial angular velocity: ω = 10 rad/s + 10 rad/s = 20 rad/s.
Angular Velocity – Angular velocity is the rate of change of angular displacement and is measured in radians per second.
Angular Acceleration – Angular acceleration is the rate of change of angular velocity and is measured in radians per second squared.
Kinematic Equation for Rotational Motion – The equation ω = ω₀ + αt relates initial angular velocity (ω₀), angular acceleration (α), and time (t) to find final angular velocity (ω).
