Question

Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.7 seconds to get up to its full speed of f1 = 78 revolutions per minute.

Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 15 times while accelerating uniformly.

Randomized Variables
t1 = 11.7 seconds
n2 = 15 times
How many revolutions does the turntable make while accelerating in Case 1?

Answer 1

The turntable makes approximately 7.615 revolutions while accelerating to its full speed of 78 revolutions per minute over 11.7 seconds in Case 1.

Step-by-step explanation:

To calculate the number of revolutions the turntable makes while accelerating in Case 1, we can use the kinematic equations of rotational motion. In uniform acceleration, the total number of revolutions (n) made by the turntable can be given by the equation:

n = ​​½ * (f1/60) * t1

Here, f1 is the final rotational speed in revolutions per minute, and t1 is the time in seconds for the turntable to reach that speed. First, we convert the final speed from rpm to revolutions per second (rps) by dividing by 60, since there are 60 seconds in a minute:

f1 = 78 rpm \u2044 60 = 1.3 rps

We then plug the values into the formula to get the number of revolutions:

n = ​​½ * (1.3 rps) * (11.7 s) = ​​½ * (1.3) * (11.7) = 7.615

The turntable makes approximately 7.615 revolutions while accelerating in Case 1.