Circular Decceleration

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In summary, the problem involved calculating the angular acceleration of a record player's turntable based on its rate of rotation and time to come to rest. The solution involved converting rev/min to rad/s and using the average deceleration formula to find the magnitude of the angular acceleration. The correct solution was 0.0573 rad/s^2.
  • #1
Problem:

The turntable of a record player rotates at a rate of 50.7 rev/min and takes 92.7s to come to rest when switched off.

Calculate the magnitude of its angular acceleration. Answer in units of rad/s^2.

Solution:

First I converted rev/min to rad/s. Which I got to be 5.309 rad/sec. Then I found the constant average decceleration which would be the decceleration because it is a constant decceleration.

A(avg)
=
The Change in Velocity
---------------------
The Change in Time

My soultion, which is wrong, is -.0573. What am I doing wrong?
 
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  • #2
Ha!

Well, it was asking for the magnitude... so the solution was .0573 not -.0573.
 
  • #3


It seems like you are on the right track but your calculation for the average angular acceleration is incorrect. To find the average angular acceleration, we can use the formula:

α(avg) = (ωf - ωi) / t

Where:
α(avg) = average angular acceleration
ωf = final angular velocity (in rad/s)
ωi = initial angular velocity (in rad/s)
t = time (in seconds)

In this problem, ωf = 0 (since the turntable comes to rest) and ωi = 5.309 rad/s. Plugging in these values and the given time of 92.7 seconds, we get:

α(avg) = (0 - 5.309) / 92.7 = -0.0573 rad/s^2

So your calculation was correct, but you just forgot to include the negative sign in your answer. The negative sign indicates that the turntable is decelerating, as we would expect.

Therefore, the magnitude of the angular acceleration is 0.0573 rad/s^2.
 

1. What is circular deceleration?

Circular deceleration is a type of acceleration that occurs when an object's velocity decreases while moving in a circular path. This means that the object's speed is decreasing, but it is still moving in a circular motion.

2. How is circular deceleration different from linear deceleration?

Circular deceleration occurs when an object's velocity decreases while moving in a circular path, while linear deceleration occurs when an object's velocity decreases in a straight line. In circular deceleration, the object's direction of motion is constantly changing, while in linear deceleration, the object moves in a straight line.

3. What causes circular deceleration?

Circular deceleration is caused by a force acting on an object that is moving in a circular path. This force, known as centripetal force, is directed towards the center of the circle and causes the object to slow down and change direction.

4. How is circular deceleration measured?

Circular deceleration is measured in units of meters per second squared (m/s²) or radians per second squared (rad/s²). This represents the change in velocity per unit of time as the object moves in a circular path.

5. How can circular deceleration be calculated?

The formula for calculating circular deceleration is a = v²/r, where a is the deceleration, v is the velocity, and r is the radius of the circular path. This formula can be used to determine the deceleration of an object moving in a circular path, given its velocity and radius.

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