The radius of the path of an object in uniform circular motion is halved. the centripetal acceleration needed if its speed remains the same is
half as great
the same as before
twice as great as before
four times as great as before

i'm pretty sure half as great is wrong.

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

snell's law

refractve index = sin incidence / sin refraction