Time of Equal Tangential & Radial Accelerations in Circular Motion

Thread starter ptejav
Start date Sep 15, 2010
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Circular Circular motion Motion Radial Time

In summary, the "Time of Equal Tangential & Radial Accelerations" in circular motion refers to the moment when an object experiences equal tangential and radial accelerations. It can be calculated by finding the intersection point between the tangential and radial acceleration curves on a graph or using the formula t = 2π√(r/a). This point is important because it signifies a change in the direction of acceleration for the object and is related to the conservation of energy in circular motion. The factors that can affect this time include the radius, speed, and centripetal force acting on the object.

Sep 15, 2010

ptejav

Homework Statement

A particle moves with a constant angular acceleration Alpha in a circular path. The time at which the magnitude of tangential and radial accelerations are equal is

Homework Equations

The Attempt at a Solution

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Sep 16, 2010

Vyse007

Hey ptejav...show us where exactly are you stuck, and what was your approach to the problem, Only then can we help you out.

Related to Time of Equal Tangential & Radial Accelerations in Circular Motion

1. What is the "Time of Equal Tangential & Radial Accelerations" in circular motion?

The "Time of Equal Tangential & Radial Accelerations" in circular motion refers to the moment when an object moving in a circular path experiences equal tangential and radial accelerations. This means that the object is accelerating both in the direction of motion (tangential) and towards the center of the circle (radial) at the same time.

2. How is the "Time of Equal Tangential & Radial Accelerations" calculated in circular motion?

The "Time of Equal Tangential & Radial Accelerations" can be calculated by finding the intersection point between the tangential and radial acceleration curves on a graph. This can also be determined using the formula t = 2π√(r/a), where t is the time, r is the radius of the circle, and a is the centripetal acceleration, which is equal to the radial acceleration at this point.

3. Why is the "Time of Equal Tangential & Radial Accelerations" important in circular motion?

The "Time of Equal Tangential & Radial Accelerations" is important because it signifies a change in the direction of acceleration for an object in circular motion. This is when the object transitions from solely accelerating towards the center of the circle to also accelerating in the direction of motion, which can affect the overall motion and velocity of the object.

4. What factors can affect the "Time of Equal Tangential & Radial Accelerations" in circular motion?

The "Time of Equal Tangential & Radial Accelerations" can be affected by the radius of the circle, the speed of the object, and the centripetal force acting on the object. A larger radius or a slower speed will result in a longer "Time of Equal Tangential & Radial Accelerations", while a smaller radius or a faster speed will result in a shorter time.

5. How does the "Time of Equal Tangential & Radial Accelerations" relate to the conservation of energy in circular motion?

The "Time of Equal Tangential & Radial Accelerations" is a critical point in circular motion where the object's kinetic energy and potential energy are equal. This is in accordance with the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. At this point, the object's energy is being converted from potential energy (at the top of the circle) to kinetic energy (at the bottom of the circle).