7.6. Uniform Circular Motion

When the velocity of an object changes, we say that the object is accelerating. The change in the velocity could be due to change in its magnitude or the direction of the motion or both.

Acceleration is defined as a change in velocity over time. This means that if an object’s speed increases or decreases, or if it changes direction, we say that it is experiencing acceleration. For example, when a car speeds up as it goes from a stop sign, it is accelerating because its speed is increasing. Similarly, if the car turns a corner at the same speed, it is also accelerating because the direction of its motion is changing.

Think of a roller coaster. As the coaster climbs higher, it slows down and then accelerates downwards when it reaches the peak. When it turns sharp corners, even if its speed remains the same, the coaster is accelerating because its direction is changing.

Can you think of an example when an object does not change its magnitude of velocity but only its direction of motion? The motion of the athlete moving along a circular path is, therefore, an example of an accelerated motion.

Uniform circular motion refers to the motion of an object moving in a circular path at a constant speed. While the speed remains constant, the velocity changes because velocity is a vector quantity that depends on direction. For instance, a car racing around a circular track keeps changing its direction, and thus, its velocity changes despite moving at a consistent speed.

Imagine you’re swinging a ball at the end of a string around in a circle. The ball maintains a constant speed as it moves around, but because it’s always changing direction, it is continually accelerating towards the center of the circle.

We know that the circumference of a circle of radius r is given by 2πr. If the athlete takes t seconds to go once around the circular path, the speed v is given by v = \frac{2πr}{t}

In uniform circular motion, the speed of an object can be calculated using the circumference of the circle (which is the distance traveled in one complete revolution) divided by the time it takes to make that revolution. The formula shows that the faster you complete a lap (less time), the higher your speed, and vice versa. For instance, if a cyclist takes 10 seconds to complete a circle of radius 5 meters, you can calculate their speed using the formula.

Consider a clock's minute hand. It travels in a circular path, making one complete rotation each hour (360 degrees). If you measured the distance the minute hand covers in this time and the time taken, you could calculate its speed. Just like the clock, if a car travels around a circular track, we can calculate its average speed based on the time taken for one lap.

There are many more familiar examples of objects moving under uniform circular motion, such as the motion of the moon and the earth, a satellite in a circular orbit around the earth, or a cyclist on a circular track at constant speed.

Many objects we encounter exhibit uniform circular motion. For instance, the moon orbits the Earth in a near circular path, exerting gravitational force that keeps it in that path. Similarly, satellites that orbit the Earth also maintain a consistent speed and direction, hence categorizing their movement as uniform circular motion.

Think of the rides at an amusement park that spin in a circle while keeping the same speed. No matter where you are on the ride, your speed remains constant, but you are constantly changing direction, illustrating uniform circular motion.

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