A remote-controlled car’s wheel accelerates at
22.7 rad/s.
If the wheel begins with an angular speed of 11.0 rad/s, what is the wheel’s angular speed after exactly twenty full turns?
To find the wheel's angular speed after exactly twenty full turns, we can use the concept of angular acceleration.
Angular acceleration is the rate of change of angular velocity. It is given by the equation:
angular acceleration = (final angular velocity - initial angular velocity) / time
In this case, the initial angular velocity is given as 11.0 rad/s, the final angular velocity is given as 22.7 rad/s, and the time is the number of revolutions.
Since we are given that the wheel completes exactly twenty full turns, we need to convert this into radians. One full turn is equivalent to 2π radians. So, twenty full turns is 20 * 2π = 40π radians.
Now, let's calculate the angular acceleration:
angular acceleration = (22.7 rad/s - 11.0 rad/s) / (40π rad)
= (11.7 rad/s) / (40π rad)
Finally, we can calculate the angular speed after exactly twenty full turns using the formula:
final angular velocity = initial angular velocity + angular acceleration * time
In this case, the initial angular velocity is 11.0 rad/s, the angular acceleration is (11.7 rad/s) / (40π rad), and the time is 40π radians.
final angular velocity = 11.0 rad/s + (11.7 rad/s) / (40π rad) * 40π radians
= 11.0 rad/s + 11.7 rad/s
= 22.7 rad/s
Therefore, the wheel's angular speed after exactly twenty full turns is 22.7 rad/s.