A Uniform rod AB of length 7m is undergoing combined motion such that, at some instant, velocities at top most point A is perpendicular to the rod and magnitude is 11 m/s. The mid point/ centre of mass ,say C, has a velocity of 3 m/s and is also perpendicular to the rod. If both the velocities...
So I first wrote the moment of inertia of the cylinder, since it says that it is thin-walled, I think that its moment of inertia is ##I=\eta mR^2##. After that I wrote the sum of torques, I think that there are three forces that cause torque, the two forces of friction, the one caused by the...
I already solved the first part, but according the my book, the answer isn't quite correct. This is what I did.
Finally, I ended up with ##a=\frac{F(r-R\cos\alpha)}{Rm(\gamma+1)}##. But according to my book, the answer is ##a=\frac{F(\cos\alpha-\frac{r}{R})}{m(1+\gamma)}##, what am I doing...
I am doing a project, but am struggling to find relationships of proportionality or formulae between my dependent variables (angular velocity, displacement, acceleration of the disc and kinetic energy of the system) and my independent variables (falling masses and then the number of winds) or...
1. Homework Statement
This problem was originally posted on Physics Problems Q&A: http://physics.qandaexchange.com/?qa=616/friction-between-two-disks
2. Homework Equations
Second Newton's law for rotation:
$$\tau = I \alpha = RF$$
3. The Attempt at a Solution
I tried to solve this...
1. Homework Statement
You buy a bottle of water in the store and place it on the conveyor belt with the longitudinal axis perpendicular to the direction of movement of the belt. Initially, both the belt and the bottle are at rest. We can approach the bottle as one cylinder with radius ##R##...
1. Homework Statement
.A cylinder P of radius rP is being rotated at a constant angular velocity ωP along positive y axis with the help of a motor about its axis that is fixed. Another cylinder Q of radius rQ free to rotate about its axis that is also fixed is touched with and pressed on P...
1. Homework Statement
A rectangular board laying on the ground of mass ##M## is pulled with a force ##F## to the right, while a cylinder of mass ##m##, radius ##R## rolls without slipping on the board. Assume there is no friction between the board and the floor.
Which way does the cylinder...
1. Homework Statement
Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 2.0 m diameter and a mass of 260 kg . Its maximum angular...
1. Homework Statement
A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with...
Consider a hollow sphere roughly the size of the moon, spun up to produce 1g of centripetal acceleration along a band at its equator (about 15000 kph)
Big stuff, I know.
I have a few questions about the implication of such a system, and I hope someone can help me find some answers!
- How tall...
1. Homework Statement
A Texas cockroach of mass 0.17 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 15 cm,rotational inertia 4.9 ✕ 10^−3 kg · m2, and frictionless bearings. The cockroach's speed (relative to the ground) is...
Imagine a person is moving at the equator in the direction opposite of the Earth's spin. How long would it take them to stop the rotation of the Earth?
Assume:
the person's "weight" = 90.718 kg,
they person's speed = 1m/s,
The Earth's "weight" = 5.972*10^24 kg,
the angular velocity of the...
Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv2 + 1/2Iω2 solving for v^2 we come up with the...
I'm creating an animation of free precession of a cuboid in GeoGebra. The axis of rotation is not one of the principal axes (but does go through center of mass).
Since it's much easier to find the angular velocity and L in the body frame, I defined the e1, e2 and e3 axes (as opposed to the...
1. Homework Statement
Two spheres are placed side by side on an inclined plane and released at the same time. Both spheres roll down the inclined plane without slipping.
(a) Using FBD, explain what force provides the torque allowing the sphere to roll down the inclined plane.
(b) Which sphere...
1. Homework Statement
so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3, I've uploaded the page here
The rotation matrix associated with 1.2a and 1.2b is
\begin{pmatrix}
\cos\theta &...
1. Homework Statement
2. Homework Equations
Moment of inertia
Torque
Angular momentum
3. The Attempt at a Solution
I think I can understand the physics of the situation. There will be a torque on the bus due to gravity while the back of it remains in contact with the cliff and it will start...
I'm trying to model a sphere having force applied at position P in the following diagram:
I know that this applied force will have an x and y component; the y component will propel it upwards, but what I am confused about is the x component of the force. I know that the x component will propel...
1. Homework Statement
A uniform rod (length = 2.4 m) of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end. The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point...
Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the...
1. Homework Statement
A block is placed inside a horizontal hollow cylinder. The cylinder is rotating with constant angular speed one revolution per second about its axis. The angular position of the block at which it begins to slide is 30° below the horizontal level passing through the center...
So I recently developed an interest in quad-rotors and was getting stated with its dynamics. I am particularly intrigued by the yaw motion of a quad-copter which comes into effect as a result of torques of the motors. When the motor torques are variable, we observe the yaw motion as result of a...
1. Homework Statement
I have a rotating platform that spins as a mass attached to a wheel rotates the larger platform. The mass accelerates to the ground which spins the platform essentially. I am trying to calculate the moment of inertia of another mass which will be attached to the rotating...
1. Homework Statement
A toy windmill consists of four thin uniform rods of mass m and length l arranged at rigth angles, in a vertical plane, around a thin fixed horizontal axel about which they can turn freely. The moment of intertia about the axel is ##I = \frac{4ml^2}{3}##.
Initially the...
1. Homework Statement
A homopolar generator consists of a metal disc of radius ##a## and a central axle which has radius ##a/4##. The disc has resistivity ##\rho## and thickness ##t##. It is rotated in a uniform magnetic field ##B## about an axis through the centre, which is parallel to ##B##...
1. The problem statement, all variables, and given/known data
Joe is painting the floor of his basement using a paint roller. A roller has a mass of 2.4kg and a radius of 3.8cm. In rolling the roller across the floor, Joe applies a force F= 16N at an angle of 35 degrees. What is the magnitude if...
1. Homework Statement
A tangential force F acts at the top of a thin spherical shell of mass m and radius R. Find the acceleration of the shell if it rolls without slipping.
2. Homework Equations
Since the shell is rolling, friction does not act at the bottom.
So equating the torque,
F*R= I*α...
1. Homework Statement
How does Fr=Ialpha work and how is it applied to a pulley with one mass attatched?
2. Homework Equations
F * r = I * alpha
I = moment of inertia
3. The Attempt at a Solution
I'm assuming F would be the tension of the pulley with the string. But how does that equation...