A 3.0cm diameter crankshaft that is rotating at 2500 rpm comesto a halt in 1.5 s.
a- what is the tangential acceleration of a ponit on thesurface?
b-how many revolutions does the crankshaft make as itstops?
For this question, what are the applicable concepts and/or laws and assumptions and/or simplifications?
a)
α = ω/t
make sure you do the conversions
b) θ = ωo t + ½ α t2
then unconvert from rads to revs
The applicable concepts and/or laws for this question are:
1. Tangential acceleration: Tangential acceleration is the acceleration component that is tangent to the circular path of an object in rotational motion. It is defined as the rate of change of tangential velocity.
2. Angular velocity: Angular velocity is the rate at which an object rotates around a fixed point. It is usually measured in radians per second.
3. Uniform circular motion: It is assumed that the crankshaft is rotating with uniform circular motion, meaning that its angular velocity remains constant.
4. Assumptions: It is assumed that there are no external forces or torques acting on the crankshaft, and that there is no slipping or sliding between the crankshaft and the point on its surface.
With these concepts and assumptions in mind, we can now proceed to solve the problem step-by-step.
For this question, the following concepts, laws, assumptions, and simplifications are applicable:
1. Tangential acceleration: This is the acceleration of an object moving in a circular path, directed along the tangent to the circle at any given point. It is denoted by "aT".
2. Uniform circular motion: The assumption in this question is that the crankshaft is rotating at a constant angular velocity, which means it is undergoing uniform circular motion.
3. Centripetal acceleration: This is the acceleration directed towards the center of the circular path. It is denoted by "aC" and is equal to (angular velocity)^2 multiplied by the radius.
4. Relationship between tangential acceleration and centripetal acceleration: In uniform circular motion, the tangential acceleration is related to the centripetal acceleration by the equation: aT = α * R, where "α" is the angular acceleration and "R" is the radius of the circular path.
5. Newton's second law of motion: This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force acting on the point on the surface of the crankshaft is responsible for bringing it to a halt.
Now, let's move on to answering the two parts of the question using the applicable concepts and laws mentioned above.