Tangential and radial acceleration of particle

In summary, the direction of the tangential acceleration in circular motion is in the direction of the velocity vector, while the radial acceleration points in the direction opposite the position vector. This means that in option d, the particle would be undergoing circular motion.
  • #1
DG1102
1
0

Homework Statement



In the case of a speeding particle undergoing circular motion:

a) the tangential acceleration is int he direction of the velocity vector and the radial acceleration points in the direction of the position vector
b)the tangential acceleration is perpendicular to the velocity vector and the radial acceleration points perpendicular to the position vector
c)the tangental acceleration is opposite the velocity vector and the radial acceleration points opposite the position vector
d)the tangential acceleration is int he direction of the velocity vector and the radial acceleration poitns opposite the position vector.

The Attempt at a Solution



I think the answer is either a or d, I'm not sure which way the radial acceleration points in this case.
 
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  • #2
The position vector points from the origin (presumably the center of the circle in this case) outward to the particle. So, ask yourself what the motion of the particle would be if it had a tangential velocity and was (a) accelerating outward and (d) accelerating inward ...circular motion is only possible in one of these two cases.
 

Related to Tangential and radial acceleration of particle

1. What is the difference between tangential and radial acceleration?

Tangential acceleration is the rate of change of velocity in the direction of motion, while radial acceleration is the rate of change of velocity perpendicular to the direction of motion.

2. How do you calculate tangential and radial acceleration?

Tangential acceleration can be calculated using the formula a = dv/dt, where dv is the change in velocity and dt is the change in time. Radial acceleration can be calculated using the formula a = v^2/r, where v is the velocity and r is the radius of curvature.

3. What factors affect the tangential and radial acceleration of a particle?

The tangential acceleration of a particle is affected by its speed and the forces acting on it. The radial acceleration is affected by the curvature of the path and the velocity of the particle.

4. How do tangential and radial acceleration relate to centripetal acceleration?

Centripetal acceleration is the combination of tangential and radial acceleration and is always directed towards the center of the circular motion. It is responsible for keeping an object moving in a circular path.

5. What applications do tangential and radial acceleration have in real life?

Tangential and radial acceleration play a crucial role in many real-life scenarios, such as the motion of a car on a curved road, the rotation of a Ferris wheel, and the orbit of a satellite around a planet. They are also essential in understanding the dynamics of objects in circular motion.

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