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 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...
I have 2 advantages of using rotational and orbital velocity of Earth in assisting easier rocket travel...
1. Uses less fuel as the rotational speed contributes to the rocket
2. Assists the rocket to easily produce the necessary escape velocity
Are there anymore adv? I can't seem to...
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
Given the following Rdisk = 2.50 cm, Raxle = 0.250 cm, Mdisk - 25.0g, Maxle = 0.750g
a. Determine the rotational inertia of a yo-yo about it's center.
b. Dervie using force and torque the expression for the linear acceleration of a yo-yo
c. Calculate the a of the yo-yo...
An 8kg mass is initally at rest on a 30 degree frictionless incline, it is attached to a hoop shaped 5kg pulley of radius 25.0cm by a massless cord. Find the tension in the cord and the acceleration of the mass using Newton's Laws.
A 5.0kg mass is initally held at rest, attached to a disk shaped 8.0kg pulley of radius 12.0cm by a massless cord. Using Newton's Laws, find the tension in the cord and the acceleration of the mass falling after it is released.
Please help
The axle of a 12.0kg solid sphere of radius 0.500m is attached to a suspended 5.00kg weight by a massless cord that passes over a frictionless, massless pulley. When the system is released, the mass drops and the sphere rolls without slipping. Find the tension in the cord and the acceleration of...
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
an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that axle is measured with the following...
Homework Statement
Uniform density rod with mass 1.2 kg, length 0.7m rotates around an axis perpendicular to the rod, with angular speed 50 rad/sec. its center moves with a speed of 8m/s.
What is the rotational kinetic energy?
Homework Equations
K= 1/2 I * V^2 (V is angular speed...
A thin slab of material of uniform density with a total mass 3.0 kg is cut in a strange shape: It is bounded by the curves y=4-x^2 and x=0. Initially it is lying in the xy plane. It is free to rotate about the y axi. A force of 8.0 Newtons is constantly applied perpendicular to the slab at the...
Homework Statement
I have a question about rotational static equilibrium. When we consider the static equilibrium of a system, I realized that most people only consider the net torque acting on the system. Why don't we need to consider the net force acting on the system?
For instance:
A...
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 merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutions per 8.00s? Assume it is a solid cylinder.
Homework Equations
\DeltaKE=Wnet=1/2(Iw2)=14211.7J...
Homework Statement
A grinding wheel is a uniform cylinder of with a radius of 8.50 cm and a mass of 0.580 kg. Calculate a) its moment of inertia about its center, and b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.0 s if it is known to slow down from 1500 rpm to rest...
Homework Statement
A spool of wire mass m and radius r is unwound under a constant force F. Assuming that the spool is a uniform solid cylinder that does not slip, show that the acceleration of the center of the mass is 4F/3m
Homework Equations
F+f=ma
f=ma-F
\tau =I\alpha=Fr-fr...
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 plyground merry go round of radius r=2m had a moment of inertia of I=250kg/m2 and is rotating at 10rpm about a frictionless verticle axle.Facing the axle a 25kg child hops onto the merry go round and manages to sit down on its edge.What is the new angular speed of the...
Homework Statement
A 45kg figure skater is spinning on the toes of her skates at 1.0 rev/s. Her arms are outstretched as far as they will go/ In this orientation, the skater can be modeled as a cylindrical torso (40kg, 20cm average diameter, 160cm tall) plus two rod-like arms (2.5kg each, 66cm...
A barbell consists of two small balls, each with mass 400 grams (0.4 kg), at the ends of a very low mass rod of length d = 35 cm (0.35 m). The center of the barbell is mounted on the end of a low mass rigid rod of length b = 0.525 m (see Figure). The apparatus is started in such a way that...
Homework Statement
A uniform solid cylinder and a uniform cylindrical shell are placed side by side at the top of an incline.If they sre released from rest and roll without slipping,
A)Determine their speeds when they reach the bottom
B)Which objet reaches the bottom first?
Homework...
Homework Statement
a restaurant sing hangs from a metal bar attached to a wall and supported by a wire. the bar has a mass of 5 kg, and a length of 1.2 m. the sign has a mass of 23 kg and hangs from 2 chains located at .3 m from each end of the bar. the wire makes a 28 degree angle with the...
Homework Statement
An inelastic uniform solid sphere of radius 'R' is sliding without rolling over a frictionless ground with a uniform velocity 'v'. A cubical plate of height r (r<R) is fixed on the ground and the sphere impinges upon the cubical plate and rolls over it. What is the minimum...
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...
[b]1. A rigid, massless rod has three particles with equal masses attached to it as shown below. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t = 0. Assume that m and d...
[b]1. A rigid, massless rod has three particles with equal masses attached to it as shown below. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t = 0. Assume that m and d...
Homework Statement
We have a rod length l with mass m. This rod is nail at its end to a wall. A putty with mass m also then collide with the rod right at the other end. The collision is perpendicular to the rod.
Question is what is the minimum velocity the putty need to travel to rotate the...
Homework Statement
A block of mass m = 9.00 kg is situated on an incline of angle θ = 51.0^{\circ} with coefficient of kinetic friction \mu_k = 0.200, and is connected to a light spring of spring constant k = 40.0 N/m via a light rope passing over a massive pulley as shown. The block is...
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 solid, uniform spherical ball rolls without slipping up a hill. At the top of the hill it is moving horizontally, and then it goes over a vertical cliff. How far from the foot of the cliff does the ball land, and how fast is it moving before it lands.
Use conservation...
Hi everyone, I'm having a little trouble trying to answer this problem. Here it is:
A force of 22.04 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s^2. Calculate the rotational inertia of the wheel.
Okay so i attempted the...
Homework Statement
A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T. The walls of the cone make an angle B with the vertical. The coefficient of static friction is between the block and...
Homework Statement
A rod (length 'l'; mass 'm') is hinged to a vertical wall and is released when it makes an angle @ with the wall. Find the magnitude of normal reaction exerted by the hinge just after the release of the rod?
Homework Equations
-
The Attempt at a Solution
I...
Homework Statement
A 7 kg bowling ball whose radius is 0.13 m is rolling directly toward you turning three times per second. What are the magnitude and direction of its rotational angular momentum about you? What is its translational angular momentum about you?
Homework Equations
L = r x...
Homework Statement
The three 280 g masses in the figure are connected by massless, rigid rods to form a triangle.
What is the triangle's rotational kinetic energy if it rotates at 6.5 revolutions per s about an axis through the center?
Values given:
Mass of each ball at the corner of the...
Homework Statement
A bullet of mass mB = 0.0115 kg is moving with a speed of 104 m/s when it collides with a rod of mass mR = 7.93 kg and length L = 1.05 m (shown in the figure). The rod is initially at rest, in a vertical position, and pivots about an axis going through its center of mass...
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
Suppose a 5.7×10^10 kg meteorite struck the Earth at the equator with a speed 3.0×10^4 m/s, making a 45 degree angle (see figure) and remained stuck.By what factor would this affect the rotational frequency of the Earth (1rev/day)?
Homework Equations
It seems...
Homework Statement
If a particle is projected vertically upward to a height h above the Earth's surface at a northern latitude θ, show that it strikes the ground at a point 4/3*ωcosθ*sqrt(8h^3/g) to the west. (Neglect air resistance and consider only small vertical heights.)
my initial...
Case in example:
If a motorbike is being riden down a steep hill and out of gear with no brakes applied; would this be more unstable than if the bike were in-gear using engine braking?
(Above condition being at the same speeds).
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...
Hi,
I have a physics assignment due, and I've been struggling with a particular question. I would really appreciate if anyone could please help.
Homework Statement
Consider the system below. The mp = 20.0 kg 'pulley' is a solid uniform sphere of radius of 0.250 m with the frictionless...
Homework Statement
Four identical particles of mass 0.717 kg each are placed at the vertices of a 3.11 m x 3.11 m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia of this rigid body about an axis that (a) passes through the...
Homework Statement
A thin plank of mass M and length l is pivoted at one end. The plank is released at 60 degrees from the vertical. What is the magnitiude and direction of the force on the pivot when the plank is horizontal.
Homework Equations
N/A
The Attempt at a Solution
So...