If a disk rolls smoothly down a ramp, the acceleration is related to its angular acceleration in such a way that It is equal to the product of the angular acceleration to the radius of the disk.
Linear acceleration is defined as the uniform acceleration caused by a moving body in a straight line. There are three equations that are important in linear acceleration depending upon the parameters like initial and final velocity, displacement, time and acceleration.
Angular Acceleration is defined as the time rate of change of angular velocity. It is usually expressed in radians per second per second. Thus, α = d ω/ d t. The angular acceleration is also known as rotational acceleration.
Its equal to the product of the angular acceleration to the radius of the disk.
This equation mean that linear acceleration and angular acceleration are directly proportional. The greater the angular acceleration is, the larger the linear (tangential) acceleration is, and vice versa.
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