Circular motion and radial acceleration

In summary, the magnitude of tangential and radial accelerations are equal at a time of 1/alpha seconds, based on dimensional analysis and using the formula ω = α*t. The tangential acceleration can be found using a derivative, while the formula for radial acceleration is not provided.
  • #1
ptejav
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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
a) 1/Alpha b) Sq.root Alpha c) 1/Sq.root Alpha d) Alpha

Homework Equations



The Attempt at a Solution


I worked more than two days on this problem but could not get answer.
 
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  • #2
This does not even require any work. Just use dimensional analysis. First figure out what the units of angular acceleration are. Since you know what the units of time are, figure out which choice yields units of seconds.
 
  • #3
So you have ω = α*t. Have you a formula for finding the tangential velocity from that? If you know calculus, you can then get the tangential acceleration easily with a derivative.

Any formula for radial acceleration?

We aren't supposed to give away solutions here - you have to give evidence of trying the problem!
 
Last edited:

1. What is circular motion?

Circular motion is the movement of an object along a circular path. This means that the object maintains a constant distance from a fixed point as it moves.

2. What is radial acceleration?

Radial acceleration is the acceleration of an object towards the center of a circular path. It is always perpendicular to the velocity of the object and its magnitude is equal to the square of the velocity divided by the radius of the circle.

3. How is radial acceleration different from tangential acceleration?

Radial acceleration and tangential acceleration are two components of the total acceleration of an object in circular motion. Radial acceleration is directed towards the center of the circle, while tangential acceleration is directed tangentially to the circle. Radial acceleration changes the direction of the velocity, while tangential acceleration changes the magnitude of the velocity.

4. What is the relationship between centripetal force and radial acceleration?

Centripetal force is the force that keeps an object moving in a circular path. It is equal in magnitude and opposite in direction to the radial acceleration of the object. This means that as the radial acceleration increases, so does the centripetal force required to keep the object moving in a circular path.

5. How can we calculate the radial acceleration of an object in circular motion?

The radial acceleration of an object in circular motion can be calculated using the formula a = v2/r, where "a" is the radial acceleration, "v" is the velocity of the object, and "r" is the radius of the circular path.

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