Name: __________________________________ Date: ________ Period: _______
Mr. Talboo – Physics
Circular Motion Sample Problems
SAMPLE A
Billy Bocephus thought of a plan to catch a
squirrel for dinner. He ties a 1.5-kg rock to a
string so that he can swing it in a circle above
his head. The string is 2.2 meters long and
while swinging, the rock makes 3 revolutions
each second.
(a) Calculate the period of the rock.
T = t / revolutions = 1 / 3 = 0.333 s
(b) Calculate the speed of the rock.
v = (2πr) / T = (2 π 2.2) / 0.333 = 41.469 m/s
(c) Calculate the centripetal acceleration of the rock.
ac = v2 / r = (41.4692) / 2.2 = 781.672 m/s2
(d) Calculate the centripetal force on the rock.
Fc = mv2 / r = ((1.5)(41.4692)) / 2.2 = 1172.508 N
(e) What path will the rock follow if released? Why?
STRAIGHT LINE PATH TANGENT TO THE CURVE
SAMPLE B
An 82-kg speed skater negotiates a turn with a
radius of 23 meters at a constant speed of 15
m/s.
(a) What force is acting as the centripetal force
in this example?
FRICTION
(b) Calculate the centripetal force acting on the speed skater?
Fc = mv2 / r = ((82)(152)) / 23 = 802.174 N
(c) Calculate the coefficient of friction between the skater’s skate and ice.
µ = Fc / mg = 802.174 / (82*9.8) = 0.998
SAMPLE C
The orbit of the Moon about the Earth is
approximately circular, with a mean radius of
3.84x108 m. It takes 27.3 days for the Moon to
complete one revolution about the Earth. Find
(a) the mean orbital speed of the Moon and
v = (2πr) / T = (2 π 3.84 x 108) / 2358720 s
= 1022.904 m/s
(b) its centripetal acceleration.
ac = v2 / r = (1022.9042) / 3.84 x 108 = 0.003 m/s2