## No problem! I'll be happy to help you with the calculation.

To find the average angular acceleration, you need to know the change in angular velocity and the time it takes for that change to occur. In this case, the record player is switched from 33rpm to 45rpm, which means the change in angular velocity is 45rpm - 33rpm = 12rpm.

First, we need to convert the angular velocity from rpm (revolutions per minute) to rad/s (radians per second), since the units for angular acceleration are rad/sec^2.

1 revolution = 2Ï€ radians, 1 minute = 60 seconds, so to convert from rpm to rad/s, we multiply by 2Ï€/60.

Change in angular velocity = (12rpm) * (2Ï€/60) rad/s = 0.4Ï€ rad/s.

Next, we calculate the time it takes for the speed change to occur, which is given as 2.0 seconds.

Now, we can calculate the average angular acceleration:

Average angular acceleration = Change in angular velocity / Time

= (0.4Ï€ rad/s) / (2.0 s)

= 0.2Ï€ rad/s^2.

So, the average angular acceleration of the record player is 0.2Ï€ rad/s^2.

To find the average tangential acceleration of a point on the turntable located 15cm from the axis of rotation, we need to use the formula:

Tangential acceleration = Angular acceleration * Radius.

The radius in this case is given as 15cm. However, it's better to convert it to meters to maintain consistent units with the tangential acceleration, which is m/s^2.

Radius = 15cm * (1m / 100cm) = 0.15m.

Tangential acceleration = (0.2Ï€ rad/s^2) * (0.15m) = 0.03Ï€ m/s^2.

So, the average tangential acceleration of a point 15cm from the axis of rotation is 0.03Ï€ m/s^2.

I hope this helps! Let me know if you have any more questions.