Question

An old fashioned LP record plays at 33 revolutions per minute. If a record player starts at rest and gets up to the correct rotational speed in 8 seconds, what was its average angular acceleration it�

Answer 1

The average angular acceleration of the record player is 0.434 rad/s².

Step-by-step explanation:

The average angular acceleration of the record player can be calculated using the formula:

Angular acceleration = (final angular velocity - initial angular velocity) / time

Since the record player starts at rest and reaches a rotational speed of 33 revolutions per minute (rpm) in 8 seconds, the initial angular velocity is 0 and the final angular velocity is 33 rpm. Converting rpm to radians per second (rad/s), we get:

Final angular velocity = 33 rpm × (2π rad/1 min) × (1 min/60 s) = 3.47 rad/s

Using the formula, we can calculate the average angular acceleration:

Angular acceleration = (3.47 rad/s - 0 rad/s) / 8 s = 0.434 rad/s²

Therefore, the average angular acceleration of the record player is 0.434 rad/s².

Answer 2

The average angular acceleration of an LP record going from rest to 33 rpm in 8 seconds is 0.43625 rad/s² after converting the rotation speed into radians per second and dividing by the time interval.

Step-by-step explanation:

The student is asking about calculating the average angular acceleration of an LP record that increases its rotation speed from rest to 33 revolutions per minute over a period of 8 seconds. To solve this, we need to convert the final angular speed to radians per second, calculate the change in angular velocity, and then divide by time to get the angular acceleration.

First, we convert 33 revolutions per minute to radians per second using the fact that 1 revolution is 2π radians and there are 60 seconds in a minute.

Angular velocity (ω) is: ω = (33 rev/min)(2π rad/rev)(1 min/60 s) = 3.49 rad/s

The initial angular velocity (ω0) is 0 rad/s since the record player starts from rest.

Using the formula for average angular acceleration (α), we have: α = (ω - ω0)/t = (3.49 rad/s - 0 rad/s) / 8 s = 0.43625 rad/s2

The average angular acceleration of the record player is therefore 0.43625 rad/s2.