Question

An object travels at a constant speed around a circle of radius 1.0 m in 1 second. What is the magnitude of its acceleration?

Answer 1

To find the magnitude of the acceleration of an object moving in a circle, we can use the formula for centripetal acceleration:

$a=\frac{v^2}{r}$

where:

• $a$ is the acceleration
• $v$ is the velocity (speed) of the object
• $r$ is the radius of the circle

In this case, the object travels at a constant speed, which means its velocity remains the same throughout the motion. Since the object completes one revolution in 1 second, the distance traveled along the circumference of the circle (the object's path) is equal to the circumference of the circle.

The circumference of a circle is given by: $C=2\pi r$

Plugging in the given values, we have: $C=2\pi (1.0\text{m})=2\pi \text{m}$

Since the object completes the circle in 1 second, the velocity is equal to the distance traveled divided by the time taken: $v=\frac{C}{t}=\frac{2\pi \text{m}}{1\text{s}}=2\pi \text{m/s}$

Now we can calculate the acceleration: $a=$