Question

A particle moves along a circular path at a constant speed. The radius of the circle is 1.64m and the distance traveled by the particle as it moves from point a to point b is 2.77m. What is the magnitude of the average angular acceleration of the particle in units of radians per second squared?

Answer 1

The magnitude of the average angular acceleration of the particle is zero.

Step-by-step explanation:

To find the magnitude of the average angular acceleration of the particle, we need to calculate the average angular velocity of the particle first. Since the particle moves along a circular path at a constant speed, the average angular velocity can be calculated by dividing the distance traveled by the radius of the circle. In this case, the average angular velocity would be 2.77m / 1.64m = 1.691 rad.

Next, we need to calculate the time it takes for the particle to travel from point a to point b. The time can be calculated using the formula:

time = distance / speed. In this case,

the time would be 2.77m / 1.691 rad = 1.639 s.

Finally, we can calculate the average angular acceleration using the formula: average angular acceleration = change in angular velocity / time. Since the particle moves at a constant speed, the change in angular velocity is zero, and therefore the average angular acceleration would be zero.