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Grayson Myers
Grayson Myers

Why Does An Object Accelerate When It Changes Direction

As mentioned earlier in Lesson 1, an object moving in uniform circular motion is moving in a circle with a uniform or constant speed. The velocity vector is constant in magnitude but changing in direction. Because the speed is constant for such a motion, many students have the misconception that there is no acceleration. "After all," they might say, "if I were driving a car in a circle at a constant speed of 20 mi/hr, then the speed is neither decreasing nor increasing; therefore there must not be an acceleration." At the center of this common student misconception is the wrong belief that acceleration has to do with speed and not with velocity. But the fact is that an accelerating object is an object that is changing its velocity. And since velocity is a vector that has both magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity. For this reason, it can be safely concluded that an object moving in a circle at constant speed is indeed accelerating. It is accelerating because the direction of the velocity vector is changing.

Why does an object accelerate when it changes direction

To understand this at a deeper level, we will have to combine the definition of acceleration with a review of some basic vector principles. Recall from Unit 1 of The Physics Classroom that acceleration as a quantity was defined as the rate at which the velocity of an object changes. As such, it is calculated using the following equation:

Note in the diagram above that there is a velocity change for an object moving in a circle with a constant speed. A careful inspection of the velocity change vector in the above diagram shows that it points down and to the left. At the midpoint along the arc connecting points A and B, the velocity change is directed towards point C - the center of the circle. The acceleration of the object is dependent upon this velocity change and is in the same direction as this velocity change. The acceleration of the object is in the same direction as the velocity change vector; the acceleration is directed towards point C as well - the center of the circle. Objects moving in circles at a constant speed accelerate towards the center of the circle.

The acceleration of an object is often measured using a device known as an accelerometer. A simple accelerometer consists of an object immersed in a fluid such as water. Consider a sealed jar that is filled with water. A cork attached to the lid by a string can serve as an accelerometer. To test the direction of acceleration for an object moving in a circle, the jar can be inverted and attached to the end of a short section of a wooden 2x4. A second accelerometer constructed in the same manner can be attached to the opposite end of the 2x4. If the 2x4 and accelerometers are clamped to a rotating platform and spun in a circle, the direction of the acceleration can be clearly seen by the direction of lean of the corks. As the cork-water combination spins in a circle, the cork leans towards the center of the circle. The least massive of the two objects always leans in the direction of the acceleration. In the case of the cork and the water, the cork is less massive (on a per mL basis) and thus it experiences the greater acceleration. Having less inertia (owing to its smaller mass on a per mL basis), the cork resists the acceleration the least and thus leans to the inside of the jar towards the center of the circle. This is observable evidence that an object moving in circular motion at constant speed experiences an acceleration that is directed towards the center of the circle.

Another simple homemade accelerometer involves a lit candle centered vertically in the middle of an open-air glass. If the glass is held level and at rest (such that there is no acceleration), then the candle flame extends in an upward direction. However, if you hold the glass-candle system with an outstretched arm and spin in a circle at a constant rate (such that the flame experiences an acceleration), then the candle flame will no longer extend vertically upwards. Instead the flame deflects from its upright position. This signifies that there is an acceleration when the flame moves in a circular path at constant speed. The deflection of the flame will be in the direction of the acceleration. This can be explained by asserting that the hot gases of the flame are less massive (on a per mL basis) and thus have less inertia than the cooler gases that surround it. Subsequently, the hotter and lighter gases of the flame experience the greater acceleration and will lean in the direction of the acceleration. A careful examination of the flame reveals that the flame will point towards the center of the circle, thus indicating that not only is there an acceleration; but that there is an inward acceleration. This is one more piece of observable evidence that indicates that objects moving in a circle at a constant speed experience an acceleration that is directed towards the center of the circle.

See Answer An object which experiences either a change in the magnitude or the direction of the velocity vector can be said to be accelerating. This explains why an object moving in a circle at constant speed can be said to accelerate - the direction of the velocity changes.

For questions #5-#8: An object is moving in a clockwise direction around a circle at constant speed. Use your understanding of the concepts of velocity and acceleration to answer the next four questions. Use the diagram shown at the right.

My maths teacher explained this to be me by way of analogy: a car driving around a perfectly circular track would be constantly changing its velocity (while the magnitude of the velocity is not changing, the direction is). Because acceleration is the rate of change of velocity, and the object is changing direction, it is said to be accelerating. This strikes me as an odd definition of acceleration, as surely it still equals $\mathrm0 ms^-2$, even if the object is changing direction. Nevermind, I thought, it's just a definition.

If it is changing direction, then its motion is changing too. This is intuitively what we understand by acceleration. For example, if you were in a vehicle which is changing its direction only, you would feel the changes in the motion of the vehicle.

What your Maths Teacher may have meant is that the object changing direction has different acceleration , in the sense that the magnitude of the acceleration is constant (provided no external force) ; it is only changing it's resultant direction .

Acceleration is defined as the rate of change of velocity. Since velocity is a vector quantity (it has both magnitude and direction) defined as speed in a particular direction, any change in either speed or direction of travel is a change in velocity. Acceleration therefore occurs whenever an object changes direction- for example, a car driving around a roundabout is constantly accelerating even if its speed does not change.

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

See Common Rebuttals Rebuttal: In the case of uniform circular motion, what is the angle between velocity and acceleration? Reply: If the speed remains constant, then the component of acceleration which is parallel to the velocity is zero. This component is called as tangential acceleration. The direction changes due to the centripetal acceleration which is radially inward. Thus, the net acceleration in the case of uniform circular motion is perpendicular to the velocity.

Air resistance: The force air exerts on something moving through it. When an object with a bigger surface falls through air, it feels more air resistance. Air resistance does not depend on the mass of the object.

Now, weight is the amount of mass times the force of gravity, or how hard a planet is pulling an object towards itself. Going back to our apple, that apple would be a lot easier to lift and put in my mouth on the Moon than on Earth, right? The Earth pulls on the apple harder than the moon would, because the pull of the Earth (gravity) is stronger than that of the Moon. Even though I have the same amount of stuff, the same mass, the weight of my apple is greater on Earth than it is on the Moon. Weight is mass times acceleration, this acceleration is from the gravity force that pulls the objects toward the ground. Weight has the unit of Newtons, which is the units of mass (kilograms) times the units of acceleration. But how do we sometimes get units of mass when we ask for the weight of things? That is because the scales we use to measure weight factor in the acceleration of the pull of the Earth on the object. This factor is a constant on the Earth, meaning that it is always the same if you are on Earth. If I were on the moon and my apple weighs .25 Newtons, I will need to know the value of the acceleration of gravity on the moon to find its mass.

Now on to velocity, speed, acceleration and force. Velocity and speed are two different things, but the difference is very small. Velocity gives more information than speed does, because it tells us how fast something is moving in a specific direction. Speed is how fast something is going, but says nothing about the direction of that motion.. Acceleration says how much the velocity is changing in a specific direction. If something has a constant velocity, say moving south at 65 mph, there is no acceleration.

When something falls, it falls because of gravity. Because that object feels a force, it accelerates, which means its velocity gets bigger and bigger as it falls. The strength with which the Earth pulls on something in the form of gravity is a type of acceleration. Earth pulls on everything the exact same amount. Everything gets accelerated towards the Earth exactly the same way. The force that objects feel may be different because they have different masses, but the acceleration on Earth they experience is exactly the same. Weight is the force that acts on the mass due to gravity, because it is how much stuff there is times the acceleration at which is pulled towards the Earth, or any planet or moons. Because Earth gives everything the exact same acceleration, objects with different masses will still hit the ground at the same time if they are dropped from the same height.


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