# The Relationship between Acceleration and Rolling Angle

The Relationship between Acceleration and Rolling Angle

## Design

The purpose of this experiment was to assess whether or not there is a directly proportional relationship with respect to the acceleration (a) of a ball descending from the height of a ramp, and the ramp’s angle (θ). It can then be inferred that an increase in the angle (θ) of the ramp, would render an increase in the acceleration (a) of the ball. If the acceleration (a) is to increase, then by Newton’s Second Law of Motion (the Law of Inertia), the increase in acceleration (a) must be a direct result of an increase in force, considering the mass doesn’t change.

Newton’s Second Law of Motion states that:

Force = (; where force = ΣFn = net force, mass is measured in kilograms, and acceleration is measured in ms-1

acceleration=

The force causing the ball to descend from the top of the slope to the bottom is the gravitational force (g). Therefore, the equation above can be rewritten

acceleration=

However, from the derivation of the formula of acceleration down the slope of an inclined plane, it can be written that

acceleration=g

The inclined plane was constructed of two meter sticks (joined together at right angles such that the ball could descend the slope), adjustable metal bars (used to set the height of the plane, and the corresponding magnitude of the angle (θ)). The plane was set up on a lab table, where the top of the table was the horizontal to the incline. A small rubber ball was used to measure the acceleration due to gravity ...