Isaac Newton studied circular motion and defined properties such as tangential acceleration. Objects in circular motion experience a centripetal force towards the center of the circle. Tangential acceleration is a factor of velocity squared and radius. People use these laws of motion daily, such as experienced drivers keeping the accelerator lightly depressed during sharp turns. Slip occurs when the centripetal force decreases, and space missions use the gravitational pull of celestial bodies to accelerate into a curved path.
Many objects travel in a circular motion. These include ice skaters, cars and planets. In the late 1600s, Isaac Newton studied circular motion and defined several new properties of these systems. Tangential acceleration is one of the components derived from him, among many.
Newton observed that an object, once in motion, will travel in a straight line unless an external force is applied. An object traveling in a circular path experiences a force that pulls or pushes towards the center of the circle, called the normal or centripetal force. None of these forces are found along the curved path. They are continuously at right angles to each other.
In linear motion, an object once set in motion will remain in motion unless driven by another force. No additional energy is required. This is not true for circular motion.
The object moving in a circle at a constant speed, measured in revolutions per minute, has a constant tangential speed and a constant angular speed. In linear motion, when velocity is constant, acceleration is zero. Tangential acceleration is positive. Energy is needed to keep changing direction all the time.
Tangential acceleration is equal to the tangential velocity squared, divided by the radius. It is also calculated from the radius times the square of the angular velocity. From these equations two observations can be made on tangential acceleration. Linear acceleration is a factor of velocity only, while tangential acceleration is a factor of velocity squared. The sensation of speed is much stronger in a cornering car than in one moving at the same linear speed in a linear direction.
Tangential acceleration is a factor of the radius. As the radius increases, the tangential acceleration decreases at the same angular velocity. Stated differently, as the radius gets smaller, with no additional energy input, the angular velocity increases.
People exploit the laws of motion applied to circular or curved paths on a daily basis. Experienced drivers slow down first and then keep the accelerator pedal lightly depressed during sharp turns. The added energy keeps the wheels forward rather than skidding sideways.
Slip occurs when the centripetal force driving tangential acceleration decreases. Ice skaters bring their arms and free leg close to their body to spin faster. Several space missions have used the gravitational pull of the moon or other celestial bodies to accelerate the space capsule into a desired curved path.
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