A turntable rotating at 78 rev/min slow down and stops in 32 second after the motor is turned off.
a) Find its angular acceleration in
rev/min^2.
b)how many revolutions does it make in this this time
To find the angular acceleration of the turntable, we need to use the formula:
Angular acceleration = (final angular velocity - initial angular velocity) / time
a) First, let's convert the final angular velocity from revolutions per minute (rev/min) to revolutions per second (rev/s).
1 minute = 60 seconds
So, final angular velocity = 78 rev/min = 78 rev/60s = 1.3 rev/s
Next, we need to find the initial angular velocity. Since the turntable is initially rotating at 78 rev/min, the initial angular velocity is the same as the final angular velocity, which is 1.3 rev/s.
Now, we can calculate the angular acceleration:
Angular acceleration = (1.3 rev/s - 1.3 rev/s) / 32 s
Angular acceleration = 0 rev/s / 32 s
Angular acceleration = 0 rev/s^2 (since the turntable has come to a stop)
Therefore, the angular acceleration of the turntable is 0 rev/s^2, indicating that it decelerates uniformly and eventually stops.
b) To find the number of revolutions the turntable makes during this time, we need to use the formula:
Number of revolutions = (initial angular velocity + final angular velocity) / 2 * time
Here, the initial angular velocity is 1.3 rev/s, and the final angular velocity is 0 rev/s. The time is 32 seconds.
Number of revolutions = (1.3 rev/s + 0 rev/s) / 2 * 32 s
Number of revolutions = 1.3 rev/s / 2 * 32 s
Number of revolutions = 0.65 * 32 rev
Number of revolutions = 20.8 rev (approximately)
Therefore, the turntable makes approximately 20.8 revolutions during this time.