A) The famous Spiro’s Spinning Pizza is accelerating with an angular acceleratio

Question

A) The famous Spiro’s Spinning Pizza is accelerating with an angular acceleration of 0.34 rad/s2 about its center. Find the tangential acceleration of an olive sitting on the pizza 8.3 cm from the center. ____m/s^2
B) A speedboat moves in a circular path with tangential acceleration 2.1 m/s2. Its angular acceleration is then 0.14 rad/s2. Find the radius of the path. ____m
C) A planet’s moon revolves around the planet with a period of 42 Earth days in an approximately circular orbit of radius of 5.2×108 m. How fast does the moon move? _____m/s
D) A railroad locomotive, moving at 7.0 m/s around a curve in the form of a circular arc, undergoes centripetal acceleration of 0.11 m/s2. What is the radius of the circular arc? _____m

E) In order to give the inhabitants near the rim of a cylindrical space station the feeling of Earth’s gravity, determine the rotational period of a station constructed with a radius of 580 m. ____s
F) Find the minimum speed of a roller coaster at the top of a vertical loop for the roller coaster to successfully negotiate the loop. The radius of the loop is 21 m. _____m/s
A) The famous Spiro’s Spinning Pizza is accelerating with an angular acceleration of 0.34 rad/s2 about its center. Find the tangential acceleration of an olive sitting on the pizza 8.3 cm from the center. ____m/s^2
B) A speedboat moves in a circular path with tangential acceleration 2.1 m/s2. Its angular acceleration is then 0.14 rad/s2. Find the radius of the path. ____m
C) A planet’s moon revolves around the planet with a period of 42 Earth days in an approximately circular orbit of radius of 5.2×108 m. How fast does the moon move? _____m/s
D) A railroad locomotive, moving at 7.0 m/s around a curve in the form of a circular arc, undergoes centripetal acceleration of 0.11 m/s2. What is the radius of the circular arc? _____m

E) In order to give the inhabitants near the rim of a cylindrical space station the feeling of Earth’s gravity, determine the rotational period of a station constructed with a radius of 580 m. ____s
F) Find the minimum speed of a roller coaster at the top of a vertical loop for the roller coaster to successfully negotiate the loop. The radius of the loop is 21 m. _____m/s

Explanation / Answer

(A) angular acceleration alpha = 0.34 rad/s2 and radius R = 0.083 m

tangential acceleration a = alpha * R = 0.34 * 0.083 =

a = 0.02822 m/s

(B) a = 2.1 m/s2 , alpha = 0.14 rad/s2

R = a/alpha = 2.1/0/14

R = 15 m

(C) Time period T = 42*24*3600 sec

T = 3628800 sec

Radius R = 5.2x108 m/s

D= 2*pie*R = 2*3.14 * (5.2 x 108)

D = 32.656 x 108 m

V = D/T

V = 899.91 m/s

V= 900 m/s

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