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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 = (41.469

2) / 2.2 = 781.672 m/s

2

(d) Calculate the centripetal force on the rock.

Fc = mv2 / r = ((1.5)(41.469

2)) / 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)(15

2)) / 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 = (1022.904

2) / 3.84 x 10

8 = 0.003 m/s

2