What Is the Rotational Acceleration in a Revolving Door?

In summary, rotational acceleration is the measure of how quickly an object's angular velocity changes as it rotates around an axis. It is different from linear acceleration, which measures changes in an object's velocity in a straight line. Rotational acceleration is caused by a force or torque not directly in line with an object's center of mass, and it is measured in radians per second squared. Real-life examples of rotational acceleration include spinning tops, merry-go-rounds, and sports movements such as figure skating and diving.
  • #1
tymartin
9
0

Homework Statement



Suppose a revolving door at the bank is spinning around once every 4 seconds. As you walk through, you push on the door for 3 seconds, which increases the rotational speed so that it rotates once a second. What wat the rotational acceleration due to your push?

Homework Equations



This is what I have so far...

The Attempt at a Solution



Acceleration-90/4=22.5

Displacement-360/3=120

22.5 + 120= 140.5 rev/s
 
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  • #3
^2

The rotational acceleration in this situation can be calculated using the formula a = Δω/Δt, where a is the rotational acceleration, Δω is the change in angular velocity, and Δt is the change in time. In this case, the change in time is 3 seconds and the change in angular velocity is 1 revolution per second, so the rotational acceleration is 1/3 revolutions per second squared (rev/s^2). This means that the door's rotational speed is increasing by 1 revolution every 3 seconds. It is important to note that rotational acceleration is a vector quantity, meaning it has both magnitude and direction. In this case, the direction of the rotational acceleration is towards the center of the revolving door, due to the push applied by the person walking through.
 

1. What is rotational acceleration?

Rotational acceleration is the rate of change of angular velocity of an object as it rotates around an axis. It is a measure of how quickly the object is speeding up or slowing down in its rotational motion.

2. How is rotational acceleration different from linear acceleration?

Linear acceleration is the rate of change of an object's velocity in a straight line, while rotational acceleration is the rate of change of an object's angular velocity as it rotates around an axis. They both measure how quickly an object is speeding up or slowing down, but in different types of motion.

3. What causes rotational acceleration?

Rotational acceleration can be caused by a torque or a force applied to an object that is not directly in line with its center of mass. This force causes the object to rotate, resulting in a change in its angular velocity and thus a rotational acceleration.

4. How is rotational acceleration measured?

Rotational acceleration is measured in units of radians per second squared (rad/s²). It can be calculated by dividing the change in angular velocity by the change in time, or by using the formula a = αr, where a is the rotational acceleration, α is the angular acceleration, and r is the distance from the axis of rotation to the point where the force is applied.

5. What are some real-life examples of rotational acceleration?

Some examples of rotational acceleration in everyday life include the spinning of a top, the rotation of a merry-go-round, and the rotation of a car's wheels when turning. It is also involved in sports such as figure skating, gymnastics, and diving, where the athlete's body experiences rotational acceleration during their movements.

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