Circular Motion Questions and Answers

as it moves in a clockwise horizontal circular path at a constant speed 8

A centrifuge rotor is accelerated for 36 s from rest to 19000 rpm revolutions per minute a What is its average angular acceleration b Through how many revolutions has the centrifuge rotor turned during its acceleration period assuming constant angular acceleration a

A bicycle slows down uniformly from Vo 7 29 m s to rest over a distance of 108 m Fig 8 9 Each wheel and tire has an overall diameter of 67 8 cm Determine the total number of revolutions each wheel rotates before coming to rest

A carousel is initially at rest At t 0 it is given a constant angular acceleration a 0 067 rad s which increases its angular velocity for 6 8s At t 6 8s determine the angular velocity of the carousel rad s

2 A tiny pin on a toy car s wheel with a radius of 2cm is travelling at a constant speed It makes ten complete revolution in 2 seconds a Sketch a graph of the height of the pin above the ground during ten complete revolutions beginning when the pin is closest to the ground Be very clear with your scale 12

5 A point on the surface of a neutron star is 32 000 m from the spin axis The s rotates at 180 revolutions per minute

J 2002B2B A ball attached to a string of length swings in a horizontal circle as shown above with a constant speed The string makes an angle 0 with the vertical and I is the magnitude of the tension in the string Express your answers to the following in terms of the given quantities and fundamental constants a On the figure below draw and label vectors to represent all the forces acting on the ball when it is at the position shown in the diagram The lengths of the vectors should be consistent with the relative magnitudes of the forces b Determine the mass of the ball C Determine the speed of the ball d Determine the frequency of revolution of the ball e Suppose that the string breaks as the ball swings in its circular path Qualitatively describe the trajectory of the ball after the string breaks but before it hits the ground

An athlete swings a 6 90 kg ball horizontally on the end of a rope The ball moves in a circle of radius 0 990 m at an angular speed of 0 550 rev s a What is the tangential speed of the ball m s b What is its centripetal acceleration m s c If the maximum tension the rope can withstand before breaking is 132 N what is the maximum tangential speed the ball can have m s

A6500kg car can produce a force 32 000 speed it can travel around a turn with a radius of Acceleration of this car be What is the coefficient of between the car and the ground 32 000 2 A Student is spinning a 0 015 kg yo yo in a horizontal circle above their head The tension in the string as the yo yo spins is measured at 10 5 N The student also measured that the diameter of the circle that the yo yo is making above their head is 3 5 m Find the velocity that the yo yo is moving at Find the acceleration of the yo yo 0 015 2x77 4 3 A 145 lb child is in the Rotor Ride while it is spinning at a speed of 70 ft s The room has a radius of 17 ft Find the acceleration of the hild in the ride Find the coefficient of friction between the boy and

m 2009Bbl An experiment is performed using the apparatus above A small disk of mass m on a frictionless table is attached to one end of a string The string passes through a hole in the table and an attached narrow vertical plastic tube An object of mass my is hung at the other end of the string A student holding the tube makes the disk rotate in a circle of constant radius r while another student measures the period P mr Derive the equation P 2 that relates P and m m 8 The procedure is repeated and the period P is determined for four different values of my where m 0 012 kg and r 0 80 m The data which are presented below can be used to compute an experimental value for g a E 11 E E ALM 21 LL H A J ILI b What quantities should be graphed to yield a straight line with a slope that could be used to determine g On the grid below plot the quantities determined in part b label the axes and draw the best fit line to the data You may use the blank rows above to record any values you may need to calculate C a m kg P s LI MITT ME 0 020 L T 1 40 0 040 W 1 05 0 060 0 80 m IL 0 080 14 0 75

Pl 1998B6 A heavy ball swings at the end of a string as shown above with negligible air resistance Point P is the lowest point reached by the ball in its motion and point Q is one of the two highest points a On the following diagrams draw and label vectors that could represent the velocity and acceleration of the ball at points P and Q If a vector is zero explicitly state this fact The dashed lines indicate horizontal and vertical directions i Point P be ii Point Q b After several swings the string breaks The mass of the string and air resistance are negligible On the following diagrams sketch the path of the ball if the break occurs when the ball is at point P or point Q In each case briefly describe the motion of the ball after the break i Point P ii Point Q

E 0 14 m 1999B5 A coin C of mass 0 0050 kg is placed on a horizontal disk at a distance of 0 14 m from the center as shown above The disk rotates at a constant rate in a counterclockwise direction as seen from above The coin does not slip and the time it takes for the coin to make a complete revolution is 1 5 s a The figure below shows the disk and coin as viewed from above Draw and label vectors on the figure below to show the instantaneous acceleration and linear velocity vectors for the coin when it is at the position shown b Determine the linear speed of the coin c The rate of rotation of the disk is gradually increased The coefficient of static friction between the coin and the disk is 0 50 Determine the linear speed of the coin when it just begins to slip d If the experiment in part c were repeated with a second identical coin glued to the top of the first coin how would this affect the answer to part c Explain your reasoning

T 0 5 kg 2m 1978B1 A 0 5 kilogram object rotates freely in a vertical circle at the end of a string of length 2 meters as shown above As the object passes through point P at the top of the circular path the tension in the string is 20 newtons Assume g 10 meters per second squared a On the following diagram of the object draw and clearly label all significant forces on the object when it is at the point P b Calculate the speed of the object at point P c Calculate the increase in kinetic energy of the object as it moves from point P to point Q d Calculate the tension in the string as the object passes through point Q

1974B1 A pendulum consisting of a small heavy ball of mass m at the end of a string of length L is released from a horizontal position When the ball is at point P the string forms an angle of 0 with the horizontal as shown a In the space below draw a force diagram showing all of the forces acting on the ball at P Identify each force clearly b Determine the speed of the ball at P P

1 An object that is moving in a circle experiences centripetal acceleration this acceleration affects which aspect of the object s velocity vector O MAGNITUDE DIRECTION

Two children Ahmed and Jacques ride on a merry go round Ahmed is at a greater distance from the axis of rotation than Jacques Which one of the following is true statement Jacques has a smaller angular speed than Ahmed Jacques and Ahmed have the same tangential speed Jacques has a greater angular speed than Ahmed Jacques and Ahmed have the same angular speed

Use g 10 m s A child that weighs 500 N swings on a swingset When the child is at the lowest point in the arc the total tension in the swing chains is 750 N What is the child s ce acceleration x m s

Multiple choice short answer 1 point for correct answer 3 points for explanation 2 An object is moving clockwise in a horizontal circle At the point it is furthest to the right in the circle draw its tangential velocity vector and its acceleration vector Make sure to label and explain

A wheel is rotating at an initial angular velocity of 8 rev s and is accelerating at a constant rate of 3 52 rad s Find the time required to reach 24 rev s Round your answer to 2 decimal places

The washing machine s spin drier with an initial angular velocity of 49 rad s is slowing down uniformly to 12 rad s while making 67 revolutions Find the time required to make 67 revolutions Round your answer to 2 decimal places

A ferris wheel with a radius of 45 feet has its center 55 feet above the ground When in operation it makes a full turn every 22 seconds Let H t be the height of a point P on the ferris wheel t seconds after it begins operation and suppose you know that P reaches the higihest point at t 30 seconds The maximum height is feet The first time P was at this height was a t seconds The next time P will be at this height will be at t seconds We can model H t using a cosine function with amplitude A phase shift least possible value of the phase shift and enter the

What happens to tangential velocity as the radius of an object increases provided the angular velocity remains the same A B C D It decreases because tangential velocity is inversely proportional to the radius It increases because tangential velocity is directly proportional to the radius It decreases because tangential velocity is directly proportional to the radius It increases because tangential velocity is inversely proportional to the radius

18 Screens 23 png Question 14 Add your answer A wheel is rotating at an initial angular velocity of 3 rev s and is accelerating at a constant rate of 2 97 rad s Find the time required to reach 26 rev s Round your answer to 2 decimal places Question 15 Screens 24 png A vinyl can turn 7 86 times within 3 03 s If it starts from rest what is its angular acceleration Round your answer to 2 decimal places Add your answer 2 Points 2 Points

Screens 23 png Question 16 Round your answer to 2 decimal places A belt passes over a wheel whose radius is 41 cm If a point on the belt has a velocity of 14 19 m s find the velocity the wheel is turning Picture2 jpg Add your answer Question 17 Screens 24 png A 110 kg object is moving in a circular path r 19 4 cm at a constant rate of 6 5 rev s Find the acceleration Round your answer to 2 decimal places Add your answer se silhus is 58 17 cm is rotating on a stationary axle Within 14 96 it uniformly spooded up from re Find the tangential acceleration of a point on its run 2 Points Question 20 3 Points

A 156 kg object is moving in a circular path r 11 9 cm at a constant rate of 8 8 rev s Find the acceleration Round your answer to 2 decimal places

A motorcycle has tires with a diameter of 44 0 cm Cruising down the highway they are rotating at 1150 rpm revolutions per minute What is the tangential velocity of the edges of the tires and hence the linear velocity of the motorcycle in m s Round your answer to 1 decimal place

A truck s wheel r 42 cm turning at 176 rev min increases its velocity to 442 rev min within 12 s Find the magnitude of the resultant acceleration of a point on the wheel s rim Round your answer to 2 decimal places

2788074 3 n jpg Question 16 Round your answer to 2 decimal places A belt passes over a wheel whose radius is 41 cm If a point on the belt has a velocity of 14 19 m s find the velocity the wheel is turning Add your answer Picture2 jpg 2790894 9 n jpg 2791522 2 n jpg A 2 Points 2791959 4 n jpg

Screens 21 png Question 11 Screens 22 png What happens to tangential velocity as the radius of an object increases provided the angular velocity remains the same A It increases because tangential velocity is directly proportional to the radius B It decreases because tangential velocity is directly proportional to the radius C It increases because tangential velocity is inversely proportional to the radius D It decreases because tangential velocity is inversely proportional to the radius Screens 23 png 2 Point Screens 24 png

Screens 23 png Question 18 Add your answer Question 19 A wheel whose radius is 58 17 cm is rotating on a stationary axle Within 14 96 s it uniformly speeded up from rest to a velocity of 751 rev s Find the tangential acceleration of a point on its rim Round your answer to 2 decimal places Screens Add your answer to radius is 58 17 cm il rotating on a stationary te Within 14 96 scil uniformly speeded up from Find the tangential acceleration of a point on Its Hum 24 png 3 Points A wind turbine whose blades are 25 m is rotating counterclockwise at a rate of 0 02 rev s It uniformly slows down until it stops after rotating for 7 1 s What is the magnitude of the linear acceleration at t Os Round your answer to 2 decimal places Question 20 3 Points

All changes saved 26 A ball is tied to the end of a length of string A student holds one end of the string and whirls it so the ball travels in a vertical circle The string is always taut The tension in the string is highest when the ball is at the bottom of the circle ascending from the bottom to the top of the circle descending from the top to the bottom of the circle at the top of the circle

2 A merry go round of diameter 18 m revolves at a rate of O 1 2 m s 7 8 m s 15 6 m s O 5 5 m s 8 3 rev min What is the velocity of a child who is seated at the outer edge of the merry go round

An object moves in a circular path at a constant speed Which of the following is true a The object s acceleration is zero because it has a constant speed b The object s acceleration is not zero and causes the object to slow down c The object s acceleration is not zero and causes the object to speed up d The object s acceleration is not zero and causes the change in the direction of the object s velocity e None from the above

A wheel of radius 0 50 m rotates with a constant angular speed about an axis perpendicular to its center A point on the wheel that is 0 40 m from the center has a tangential speed of 2 0 m s Determine the angular speed of the wheel 1 0 rad s 2 0 rad s 5 0 rad s 0 90 rad s 0 40 rad s

How long does it take for a rotating object to speed up from 15 0 rad to 33 3 rad s if it has an angular acceleration of 3 45 rad s 9 57 S 10 6 s 63 1 s 4 35 s

A circular disk of radius 0 200 m rotates at a constant angular speed of 3 00 rev s What is the centripetal acceleration in m s2 of a point on the edge of the disk Your Answer

A 1250 kg vehicle travels at a constant speed of 5 00 m s around a circular track that has a radius of 130 0 m Determine the magnitude of the centripetal force in N that acts on the vehicle Your Answer

A satellite of mass M takes time 20 hrs to orbit a planet If the satellite had twice as much mass the time for it to orbit the planet would be 20 hrs 80 hrs 10 hrs 5 hrs

A car enters a horizontal curved roadbed of radius 50 0 m The coefficient of static friction between the tires and the roadbed is 0 20 What is the maximum speed with which the car can safely negotiate the unbanked curve 5 0 m s 98 m s 22 m s 9 9 m s 40 m s

A ball moves with a constant speed of 4 0 m s around a circle of radius 0 25 m What is the period of the motion 1 0 s 0 25 s 0 70 s 0 39 s O 0 10 s

8 An ice skater going into a spin rotates with an angular velocity of 27 Rad sec How many revolutions will the skater make each second 9 A motor is rotating with an angular velocity of 285 Rad sec What is the angular velocity of this motor in RPM s 10 A wheel which has a radius of 14 cm is rotating with an angular velocity of 25 Rad sec What will be the linear velocity of a point on the outer edge of the wheel 11 An automobile is moving with a velocity of 22 m s The tires on the car have a diameter of 78 cm What will be the angular velocity of the wheels on this car

thac What is the centripetal acceleration of automobile driving around a circular radius 23 0m if it takes the car get around once in m s 2

The planet Mars has a mass of 6 420 x 1023 kg is 2 280 x 1011 meters from the sun and takes 5 936 x 107 seconds to orbit the sun in a circular orbit What speed doe the planet have as it orbits

What is the centripetal force acting on a 2000 kg car that experiences a 2 3 m s2 inward accleration as it drives around a hairpin turn

Homework Problems Find t f w VT and ac 1 A ball on the end of a 1 2 m long string is moving around a circular path at a constant rate of 6 8 radians sec

Two wheel gears are connected by a chain The larger gear has a radius of 6 centimeters and the smaller gear has a radius of 4 centimeters The smaller gear completes 28 revolutions in 15 seconds What is the linear velocity of each of the gears in centimeters per minute The linear velocity of the smaller gear is 2247 centimeters per minute The linear velocity of the larger gear is 0 56T centimeters per minute 15 O The linear velocity of the gears is the same The linear velocity is 8967 centimeters per minute The linear velocity of the smaller gear is 8967 centimeters per minute The linear velocity of the larger gear is 2247 centimeters per minute O 567 The linear velocity of the gears is the same The linear velocity is 15 centimeters per minute Y 2 3 4 5 Next

How are linear velocity and angular velocity related Drag a word phrase or equation into each box to correctly complete the statements Angular velocity is the change in distance over time where distance is Angular velocity is represented as Linear velocity is the change in can be represented by V This means that linear velocity is the 13 40 34 t or V ro t of the radius and the angular velocity W where the distance is the circumference of a circle It re t V 0 t product K quotient

15 The diagram below shows a rock on the end of a string being whirled around in a circle in the horizontal plane The motion is viewed from above and the stone is rotating clockwise What are the directions associated with its instantaneous velocity and instantaneous acceleration respectively N C W a south east ST S E b east west c south south d west west e south west 16 Imagine you are a passenger upside down at the top of a vertical looping roller coaster The centripetal force acting on you at this position a is perhaps the least of anywhere in the loop c is supplied partly by the seat of the roller coasterd is directed vertically downward e all of the above b is supplied at least partly by gravity

Through how many radians does a 33 rpm turntable rotate in 0 32 s rpm stands for revolutions per minute 8 3 rad 1 1 rad 5 2 rad 0 74 rad

To prepare a weaving loom you wind a length 2 0 m of yarn onto a reel of radius 3 0 cm This takes a time of 9 5 s What is the angular speed of the reel rad s