This document contains 6 problems about circular motion. Problem 1 discusses a car rounding a bend and losing centripetal force when hitting an oil slick, causing it to travel in a straight line. Problem 2 calculates frequency and period from revolutions and time. Problem 3 calculates speed and centripetal acceleration for a fairground ride. Problem 4 does similar calculations for a mass whirled in a circle. Problems 5 and 6 calculate forces, speeds, and accelerations for carts on a circular track and an ice skater spun by another skater.

1. 12 PHYSICS CIRCULAR MOTION ASSIGNMENT Name
1. A car is travelling around a bend in the road and for a few seconds is in uniform
circular motion.
(a) The centripetal force is being provided by the road. Name this force.
friction
The car passes over a patch of oil while it is rounding the bend.
(b) Describe the path the car will take after it hits the oil patch and explain why this
happens in terms of the forces acting.
The car travels in a straight line after hitting the oil. This happens
because friction, which was providing the centripetal force, has
disappeared. Without a centripetal force the direction of the car cannot
change and so it travels in a straight line at a constant speed.
2. An object in uniform circular motion completes 10 revolutions in 0.4 seconds
(a) Find the frequency of this motion.
f = the number of revolutions per second = revs = 10 = 25 Hz
time 0.4
(b) Find the period of this motion.
T = 1 = 1 = 0.04 s
f 25
Monday, 3 May 2010

2. 3. A big wheel at a fair spins in a circular path of radius 20 m. Once the wheel has
reached a steady speed, a student times each revolution at 13 seconds.
(a) Calculate the circumference of the big wheel.
C = 2π r = 2 x π x 20 = 125.66 ~ 130 m
Hence calculate the speed of the big wheel.
v = 2πr = 130 = 10 ms-1 (2 sf)
T 13
(b) Calculate the centripetal acceleration of each passenger.
a = v2 = 102 = 5.0 ms-2 (2 sf)
r 20
4. In a circular motion experiment, a mass is whirled around a horizontal circle which
has a 0.50 m radius. A student time 4 revolutions to take 2.0 s.
(a) Calculate the speed of the mass around the circle.
v = 2πr T = 1 = 2 = 0.5 s v = 2π x 0.5 = 6.3 ms-1
T f 4 0.5
(b) What is the direction of the velocity of the mass?
At a tangent to the circular path
(c) Calculate the centripetal acceleration of the mass.
a = v2 = 6.28322 = 79 ms-2
r 0.5
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3. (d) What is the direction of this acceleration?
Towards the centre of the circular path (in this case, towards the tube)
(e) How does the value of the centripetal acceleration compare to the acceleration
of gravity?
Gravitation acceleration = 9.8 ms-2. The calculated
acceleration (79 ms-2) is about 8 x greater
5. Two students go to a fun park for a day where they pay to drive carts around a
circular track. The track has a radius of 31.8 m and once the carts are at a
maximum speed they complete a lap in 16 s.
(a) What is the frequency of the cart’s motion when
ans to (e)
travelling at maximum speed?
The question gives T = 16 s. Frequency, f = 1/16 = 0.06 Hz
(b) When travelling at maximum speed, calculate the
speed of the cart.
v = 2πr = 2 x π x 31.8 = 13 ms-1
T 16
(c) Calculate the acceleration of the cart when travelling at maximum speed.
a = v2 = 12.48782 = 4.9 ms-2
r 31.8
Monday, 3 May 2010

4. The cart has a mass of 150 kg and one of the students, Chris has a mass of 75 kg.
(d) Calculate the size of the force acting on Chris and his cart at maximum speed.
F = ma = (150 + 75) x 4.904 = 1103.4 ~ 1100 N
(e) Chris drives over a patch of oil and loses control of his cart whilst travelling at
this maximum speed. On the diagram, draw his path after driving through the
oil.
After driving through the oil Chris veers off at a tangent to the
circular path and continues to travel in a straight line.
6. Jon and Ana are two ice-skaters. In a practiced skating move, Jon spins Ana around
in a horizontal circle.
Ana moves in a circle
as shown: Jon
Ana
(a) Draw an arrow on the diagram to show the direction of the tension force that
Jon’s arm exerts on Ana at the instant shown.
(b) If the radius of the circle is 0.95 m and the tension force in Jon’s arm is
5.00 x 102 N, calculate the speed with which Ana (55 kg) is travelling around the
circle. Give your answer to the correct number of significant figures.
F = mv2 v = Fr = 500 x 0.95 = 2.9388 ~ 2.9 ms-1
=>
r m 55
Monday, 3 May 2010

5. (d) While Ana is still moving in a circle on the ice, Jon lets her go.
(i) Describe her velocity (speed and direction) after he releases her.
her velocity (speed and direction) become constant as she veers off at a
tangent to the circular path the instant that Jon lets her go.
(ii) Explain why Ana travels with this velocity.
Anna travels with a constant velocity because now there is no longer a
force to change the direction of her velocity. Her speed remains
unchanged.
Monday, 3 May 2010