The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 2.20 s. How long does it take door B (also starting from rest) to rotate through the same angle?
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 2.20 s. How long does it take door B (also starting from rest) to rotate through the same angle?
![The image illustrates two scenarios depicting the application of force on doors with different axis placements:
1. **Door A:**
- The axis (pivot point) is positioned at the far left of the door.
- Force \( \vec{F} \) is applied downwards at the far right end of the door.
2. **Door B:**
- The axis is located at the midpoint of the door.
- Force \( \vec{F} \) is applied downwards at the far right end of the door.
**Analysis:**
- In Door A, the distance from the axis to where the force is applied (lever arm) is greater, which results in a larger torque.
- In Door B, the lever arm is shorter because the axis is in the center, resulting in less torque compared to Door A for the same amount of applied force.
This comparison highlights the impact of the position of the axis on the rotational effect (torque) of an applied force.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F172b3f26-ac3d-45cf-8c49-05893ecd4cea%2F1c0eee76-f511-4186-85cd-14cfdc292268%2F0aei2y_processed.gif&w=3840&q=75)
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