Instructions: Work the following sample problems over basic circular motion equations. Write the complete equation you used to solve the problem, show how you set up the numbers, solve for the unknown, and indicate your final answer
with units.
1) A) Baron Blade, a mad scientist, is putting the finishing touches on his latest invention. He uses a 0.03 m radius
cutoff wheel that spins up from rest to a high rate of 7,500 rpm (revolutions per minute) in 0.2 seconds. What was its angular acceleration in that time period?
B) What was the linear acceleration of a point on the edge of the cutoff wheel during that time period?
C) The cutoff wheel's motor is of course broken and it does not immediately stop when the trigger is let go (like safety is even a consideration for mad scientists... that's why they're mad!). It has an acceleration of -85 rad/s². How many seconds does it take to stop assuming he doesn't try to stop it himself in impatience?
2) A) A 4 meter diameter carnival ride alternates spinning at high and low speeds to give riders a bit of "fun disorientation". The ride starts off on the low speed setting of 1.2 rotations per second and is capable of an
instantaneous maximum angular acceleration of 4.8 rad/s2. If it takes the ride 0.43 seconds at this angular acceleration to reach the high speed, what is the high angular velocity?
B) If a rider is held against the wall of the ride (assume the maximum possible radius neglecting the thickness of
the walls), what would their linear acceleration be during the speedup process?
C) Taking the rider above, what would their linear velocity have been before speeding up? What would their linear velocity have been after speeding up? (I'm mainly asking this because A) linear velocity of a turning object
is incredibly important for the next unit and B) I'm curious if I picked sane numbers... we may have had a death in the amusement park this day...)