(1) That's the condition for rolling without slipping.chloechloe said:use alpha = a/r
(2) That's Newton's 2nd law applied to translation.ma = mg sin theta - fs;
This is an attempt to apply Newton's 2nd law to rotation, but alpha was left out of the right hand term. It should be:T = fs*r = I*alpha = (2/5)mr^2;
(4) Combine 1 and 3 to get this.fs = (2/5)ma
Combine 4 with 2 to get this.a = (5/7)g sin theta
Rotational acceleration to linear acceleration is the conversion of rotational motion to linear motion. It is a measure of the change in velocity of an object moving in a circular path, which can be translated into linear acceleration along a straight line.
The formula for calculating rotational acceleration to linear acceleration is a = r * α, where a is the linear acceleration, r is the radius of the circle, and α is the angular acceleration. This formula is derived from the relationship between the linear and angular velocities of an object in circular motion.
Examples of rotational acceleration to linear acceleration can be seen in everyday objects such as bicycle wheels, car tires, and spinning tops. In these cases, the rotational motion is converted into linear motion, allowing the objects to move in a straight line.
Rotational acceleration to linear acceleration is closely related to centripetal force, which is the force that keeps an object moving in a circular path. Centripetal force is directly proportional to the square of the object's linear speed and inversely proportional to the radius of the circular path.
The factors that affect rotational acceleration to linear acceleration include the object's mass, the radius of the circular path, and the angular acceleration. The direction and magnitude of the linear acceleration also depend on the direction and magnitude of the angular acceleration.