A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a
Practice Questions
Q1
A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?
20 rad/s
10 rad/s
30 rad/s
0 rad/s
Questions & Step-by-Step Solutions
A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?
Correct Answer: 20 rad/s
Step 1: Identify the initial angular velocity. In this case, it is 10 rad/s.
Step 2: Identify the angular acceleration. Here, it is 2 rad/s².
Step 3: Identify the time duration for which the wheel accelerates. This is 5 seconds.
Step 4: Use the formula for final angular velocity: Final angular velocity = Initial angular velocity + (Angular acceleration × Time).
Step 5: Substitute the values into the formula: Final angular velocity = 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 this result to the initial angular velocity: 10 rad/s + 10 rad/s = 20 rad/s.
Step 8: Conclude that the final angular velocity after 5 seconds is 20 rad/s.
Angular Velocity – The rate of rotation of an object, measured in radians per second.
Angular Acceleration – The rate of change of angular velocity, measured in radians per second squared.
Kinematic Equation for Rotational Motion – The equation used to calculate final angular velocity based on initial angular velocity, angular acceleration, and time.
