Question

In an experiment, students roll several hoops down the same incline plane. Each hoop has the same mass but a different radius. Each hoop rolls down the incline without slipping. Which of the following graphs best shows the linear speed V of the hoops at the bottom of the incline as a function of the radius r of the hoop?

Answer 1

Answer:

The graph should have velocity (v) on the y-axis and radius (r) on the x-axis. It will have a straight, horizontal line that goes across the graph.

Explanation:

$KE=\frac{1}{2} I(omega)^{2}$

Shown above is the formula for Kinetic Energy in rotational terms. I'm new to brain.ly so I couldn't insert the omega symbol, sorry about that. Omega can be replaced with $\frac{v^{2} }{r^2}$. Moment of Inertia (I) can be replaced with $mr^2$.

The equation becomes $KE=\frac{1}{2} mr^2(\frac{v^2}{r^2} )$ .

The r's cancel out, making the different radii negligible, causing a straight horizontal line.