What is Rotational motion: Definition and 610 Discussions
A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.
Homework Statement
Two blocks A and B are attached to a spring of force constant K and are placed on a horizontal surface. The coefficient of friction between block A and surface is zero while between block B and surface is μ. A spherical ball of mass M, radius R impinges on block A with...
Hi guys,
I need to model a ball rolling on an incline plane, and i would like to be able to calculate acceleration due to gravity for a given angle.
Currently i have:
a = f / m
f = m*g*sin(angle)
a = g*sin(angle)
I am aware this does not take rotational motion into account, which is what...
A car is moving foreword with a constant acceleration. I know the point of the tire in contact with the ground has a velocity of 0 (relative to the ground). Is the tangential acceleration at this point also zero? I came across an example problem in my text where this occurs and and it does not...
Homework Statement
A slender rod shown in the figure has a mass m and length l and is released from rest when theta=0 degrees. The horizontal and vertical components of force which the pin at A exerts on the rod at the instant shown in the figure is ?
The Attempt at a Solution
I have some...
Hi everyone!
I wanted to know if there is a possible way for a human-being to create a rotational motion of
water in a metallic box by himself, probably using his own electric field (is there such a thing?)
with no other accessories? It might be related to the term "Electric people"...
Technically this is a homework question because it's from an assignment I'm doing as practice for my exam tomorrow.
Imagine a rod standing on a table, the base of the rod is attached to the table with a hinge, so that the rod is able to swing between standing position and parallel with the...
Homework Statement
An inelastic uniform sphere of radius 'a' is sliding without rotation on a smooth horizontal plane when it impinges on a thin horizontal rod at right angles to its direction of motion and at a height 'b' from the plane. Find the maximum velocity so that it will just roll...
we have many accelerations in rotational motion ,and I don't know the difference between them. first the linear acceleration which as I understand is the vector acceleration which has the same direction as the change of velocity and it affects the speed and direction then it's two components are...
Homework Statement
Two spherical bodies with equal mass m1=m2=1000 kg are orbiting around a common barycenter in a weightless environment because of the gravitational attraction.
A: Show how the frequency of orbiting is related to the distance between two bodies.
B: We connect two...
Homework Statement
A 16.0 kg bucket of water of is suspended by a rope wrapped around a pulley, which is just a solid cylinder 0.300 m in diameter with mass 12.0 kg. The cylinder is pivoted on a frictionless axle through its center. The bucket is released from rest at the top of a well and...
Homework Statement
A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. (Consider up and to the right to be the positive...
Homework Statement
I;m trying to prove if this guy is guilty or not, after crashing on a curve. This is mulitpart, but i will only do one at a time to not confuse. The first thing I have to do is find the coefficient of static friction. I have a drag sled test, which required a force of 42...
Homework Statement
A hoop rolling on a horizontal surface with a speed v=3.3m/s when it reaches a 15 deg incline.How far up the incline does it go?How long will it be on the incline before it reaches the botttom?
Homework Equations
I=mr2
conservation energy going up=2gyf=r2+vi2...
Homework Statement
A giant yo-yo of mass 400 kg measuring about 1.2 m in radius was dropped from a platform 63 m high. One end of the string was tied to the platform, so the yo-yo unwinds as it descended. Assuming that the axle of the yo-yo has a radius of .1 m, find the velocity of descent at...
What force does work on a ball as it is rotating down an inclined plane? Explain why the other forces the ball experiences do not do work.
I think the ball experiences gravitational, normal, and frictional forces. Is the force that actually does work on the ball just gravity? I'm having a...
Four children stand at the edge of a circular horizontal platform that is free to rotate about a vertical axis. Each child has a mass of 35 kg and they are at positions that are a quarter-circle from each other. The platform has a moment of inertia equal to 500 kg*m^2 and a radius of 2.0 m. The...
Homework Statement
A pulley with mass Mp and a radius Rp is attached to the ceiling, in a gravity field of 9.81 m/s2 and rotates with no friction about its pivot. Mass M2 is larger than mass m1. T3 holds the pulley. The quantities Tn and g are magnitudes.
(Select T-True, F-False, G-Greater...
Homework Statement
At a particular moment in a race, a car moving around a turn with a radius of 50m had an angular speed of .6rad/sec and an angular acceleration of .2rad/sec2
At this particular moment find:
the linear speed
the centripetal acceleration
its total linear acceleration...
Homework Statement
A centrifuge rotor is acceleratedfrom rest to 20,000 rpm in 5min.
Through how many turns has the centrifuge rotor turned during its acceleration period?Assume constant angular acceleration.
Homework Equations
The Attempt at a Solution I just concluded that it...
Homework Statement
My lab book list these four Rotational motion equations and doesn't say what they are. Could someone please tell me what each equation is and what they are used for. thanx
Homework Equations
\theta2-\theta1=(w1+w2)(t2-t1)/2
w2-w1=alpha(t2-t1)...
Homework Statement
A spherical asteroid with radius r = 123m and mass M = 2.50×10^10kg rotates about an axis at 4 revolutions per day. A "tug" spaceship attaches itself to the asteroid's south pole (as defined by the axis of rotation) and fires its engine, applying a force F tangentially to...
A car with a weight of 10,500 N rounds a curve with a radius of 102 m on a level road at 44.0 m/s. The tires are at the point of starting to skid at this speed.
a. What is the maximum force of static friction?
b. What is the coefficient of static friction between the tires and the road?
Homework Statement
In the figure, two blocks, of masses 2 kg and 3 kg, are connected by a light string which passes over a pulley of moment of inertia 4.00 E-3 kg m m and radius 0.05 m. The coefficient of friction for the table top is 0.30. The blocks are released from rest. Using energy...
Homework Statement
A high-speed flywheel in a motor is spinning at 450 rpm when a power failure suddenly occurs. The flywheel has mass 36.0 kg and diameter 70.0 cm. The power is off for 34.0 s and during this time the flywheel slows due to friction in its axle bearings. During the time the...
There is a fairground ride where chairs connected to chains swing around. (See attachment for diagram).
The length of the supporting chains is 3m
The length of the top beam to the centre is 2m
The supporting chains make an angle of 25 degrees to the vertical.
A) What is the speed of rotation...
Homework Statement
A puck of mass m is attached to a cord that passes through a hole in a horizontal frictionless surface. The puck is originally moving in a circle of radius r and speed v. The cord is then slowly pulled from below, decreasing to a circle with radius r1. What is the work done...
This last problem set my professor gave has left me befuddled. I feel like I am missing some intuition to solve these problems. The book isn't helping much, as I have spent hours in it. I have a few problems that I need some kind of head start on.
Homework Statement
You are designing a...
Homework Statement
A merry-go-round has a radius of 5 meters and an angular velocity of 1/4 pii radians per second. How long does it take the merry go round to make one revolution? How many turns per min?
Homework Equations
radius of 5 meters and an angular velocity of 1/4 pii radians...
Homework Statement
A tradesman sharpens a knife by pushing it against the rim of a grindstone. The 35 cm diameter stone is spinning at 200 rpm and has a mass of 15 kg. The coefficient of kinetic friction between the knife and the stone is 0.20.
If the stone loses 10% of its speed in 10 s of...
Homework Statement
A computer disk is 8.0 cm in diameter. A reference dot on the edge of the disk is initially located at The disk accelerates steadily for 0.50 s, reaching 2000 rpm, then coasts at steady angular velocity for another 0.50 s.
I have found that a_t=17 m/s^2 @ .25s
a_c =...
Homework Statement
When a car is decelerating it's speed reduces from 80 km/h to 55 km/h. In this time the wheels of car complete 55 rotations. The diameter of the wheel is 1m.
Find the
1) angular acceleration of the car.
2) time taken to stop the car if it continued in same deceleration...
Homework Statement
The acceleration 'a' of the supporting surface required to keep the centre G of the circular cylinder in a fixed position during the motion, if there is no slipping between the cylinder and the support will be?Homework Equations
The Attempt at a Solution
The torque acting...
1)The torque of the weight of anybody about any vertical axis is 0. Is it always true?
2)A sphere rolls on a horizontal surface. Is there any point of the sphere which has a vertical velocity?
3) When several forces acts on a particle we take the torque of the resultant force. Is this...
I have asked this question before, but couldn't get a satisfactory response.
Let me make the problem more concise.
We have a two particle system, i.e. two masses of mass m each joined together by a spring of spring constant k.
A force F is applied to one of these particles in a direction...
Please help...rotational motion
Homework Statement
A stuntman swings from the end of 4 m long rope along the arc of a vertical circle. If his mass is 70kg, find the tension in the rope required to make him follow his circular path, assuming he starts from rest when the rope is horizontal...
Homework Statement
A penny is placed on an LP record that is slowly accelerating up to 78 revolutions per minute. It is found that if the penny is placed at 0.080m or greater from the center, then the penny slides off the edge of the record. Find the coefficient of static friction if the...
Homework Statement
The turntable of a record player rotates at 33.33rev/min and takes 20.0s to reach this speed from rest. Calculate: a) its angular acceleration, b) the number of revolutions it makes before reaching its final speed.
Homework Equations
angular acceleration = angular...
Homework Statement
The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.63 m and 0.99 m, respectively. The respective rotational speeds are 459 rev/min and 4132 rev/min. Calculate the speeds of the tips of both rotors.
Homework Equations
V=Rω
The...
I concluded that ((mv^2)/r)-(mg) was equal to the normal force but the answer says its equal to ((mv^2)/r)-(2mg). Could someone explain why to me please?
"A half sphere of radius r is fixed to a horizontal floor. The inner surface is smooth. A small ball of mass m is at the bottom of the...
Linear and Rotational Motion
A load of mass 60kg is hoisted vertically by means of a light rope running over a pulley and is accelerated from 3 to 6m/s while traveling through a distance of 6 meter. If the resistance due to friction is 50N determine
A) The pulling force in the rope
B)...
Homework Statement
A 5kg mass and a 10kg mass are connected by a rope and hung over a pulley. The pulley is a disc with a mass of 5kg and a radius of 10cm. the two masses are initially at rest with the 10kg mass 50cm higher than the 5kg mass.
Find, The speed of each mass at the instant they...
Hi, all
Homework Statement
A plain is flying at a constant velocity v=3 km/s at a constant height above the surface of the Earth, from point A on a Latitude which forms an angle of 20 degrees with the North Pole, to point B which is 5 km north to A.
Assuming that B is very close...
Homework Statement
We have a rule of mass m and length l lying on a table without friction.
We give a boost I to the rule at a distance d from the center of mass so that it now has a rotation and a translation.
1) The rule rotates about which point?
2) Determine the velocity, vm, of the...
1.1. What are the SI units of angular velocity? Why?
2. Imagine a baton twirler is spinning a baton about its center. Which would increase its rotational kinetic energy more: doubling the angular velocity of the baton while keeping the mass and length the same, or doubling the length of the...
Homework Statement
[PLAIN]http://carlodm.com/phys/1.png
Homework Equations
Energy Equation
The Attempt at a Solution
As shown in the scan.
Is this the correct approach? I have a feeling that the velocity, v, needs to be used. I used the Energy Equation for this problem but...
Homework Statement
A roller coaster vehicle has a mass of 500 kg when fully loaded with passengers. a) if the vehicle has a speed of 20.0 m/s at point A, what is the force of the track on the vehicle at this point (point a sits at the bottom of a drop of the roller coaster where the radius is...
Homework Statement
A ring of mass M is hung from the ceiling. At the top of the ring are two smaller rings of mass m. There is no friction between the big and small rings. If two smaller rings slip down the big ring, for what value of m will the big ring move upward. A picture is attached to...
1.A centrifuge rotor rotating at 5000 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.60 m·N. If the mass of the rotor is 4.70 kg and it can be approximated as a solid cylinder of radius 0.0780 m, through how many revolutions will the rotor turn before...
Homework Statement
Two cars race around a circular track. Car A accelerates at 0.340 rad/s2 around the track, and car B at 0.270 rad/s2. They start at the same place on the track and car A let's the slower-to-accelerate car B start first. Car B starts at time t = 0. When car A starts, car...
I ran across this problem studying for my exam, and I'm not sure how to solve it:
Homework Statement
A thin rod of Mass M and length L is supported by a pivot a distance of L/4 from its left end. A second support a distance 3L/4 from the left end prevents it from falling. A clay ball of...