Chapter 16, Problem 1PLA

If a particle moves in a circle of radius R at constant speed υ, its acceleration is (a) directed toward the center of the circle. (b) equal to υ²/R. (c) caused by the fact that the direction of the velocity vector changes continuously. (d) all of the above are true.

To determine

The description of acceleration for a particle moves in a circle at constant speed.

Answer to Problem 1PLA

Option (d) all the above are true.

Explanation of Solution

For a particle moving in a circle, the velocity vector always changes and tangent to the circle. And for the particle moving at constant speed, the length of the vector remains the same.

Acceleration is defined as the change in velocity per unit time. And the change in velocity of the particle always points towards the center of the circle.

Write the formula for acceleration of a particle moving in circle at constant speed

    $a=\frac{v^2}{R}$

Here, $a$ is the acceleration, $v$ is the velocity and $R$ is the radius of the circle.

Conclusion:

1. (a) From above equation, $a=\frac{v^2}{R}$. Therefore, option (a) is correct.
2. (b) The change in velocity of the particle is directed towards the center. Therefore, the acceleration vector is directed towards the center. Option (b) is correct.
3. (c) The particle moving in constant speed in a circle. Therefore, the velocity vector must be continuously changed to keep the particle in circle. Thus, option (c) is correct.
4. (d) All the above options are correct. Option (d) is correct.