1. ### I Why does wind blow leaves in circles?

Earlier today I realized that, when a strong gust of wind would blow through my area, it would pick up leaves off the ground and typically blow them in circular patterns, and typically the leaves would go in at least several complete circles before coming to rest back down on the ground. Why is...
2. ### Rotational Dynamics - Modeling brake caliper deceleration of a chassis

I am a junior engineer tasked with modeling the dynamics of a small research UAV after landing. The UAV has 3 tires, 1 on the nose landing gear and 2 on the rear landing gear. The rear tires are equipped with disc brake calipers. My coworker has explained that the simplified model (MODEL 1...
3. ### Rotational dynamics and the conservation of energy

I = Icm + mr^2 I = 0.5 mr^2 + mr^2 I= 3/2 mr^2 By COE, mgh = 0.5(3/2 mr^2)(w^2) g(2r) = 3/4(r^2)(w^2) 8g/3 = rw^2 = v^2 / r v = sqrt( 8gr/3) v=0.511m/s ans: v=0.79m/s
4. ### Rotational dynamics: Resolving forces

Resolving the weight of the cylinder c, i get Mgcosθ (-y) and Mgsinθ (-x) mgsinθ - Fs - T = ma ---(1) (where Fs is frictional force and T is tension) τ = I α (where τ is torque and α is angular acceleration) torque is produced by both tension and frictional force (T-Fs) * r = 0.5 m r^2 α...
5. ### Difference between curvilinear and rotational motion

The solution states that there's no rotational motion when ##C## is cut (the motion is curvilinear), so we can take torques with respect to the centre of mass of the plate. But, isn't it rotating? I think of it as a pendulum, which describes a circular motion. What's the difference? Wouldn't the...
6. ### I Conservation of angular momentum and its counterpart for linear momentum

Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds! --------------------------- I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...
7. ### I Moment of inertia where mass and torque are at a different positions

The formula for moment of inertia is: I=mr^2 A common derivation for this is: 1. F=ma 2. τ=rma 3. τ=rmrα = r^2 mα This is a rotational version of Newton’s second law, where torque replaces force, moment of inertia replaces mass, and angular acceleration replaces tangential acceleration...
8. ### Problems with this rotational motion question (ant walking around a rotating ring)

I've marked correct answers above. Have a look at the solutions: How is the first equation justified? Shouldn't v2 and ωR be of opposite signs? What is v1? And how is it equal to v2? My biggest problem is the source of v1 since the ring is not having vertical displacement, then what is v1?
9. ### Stabilizer Leg Linear Actuator Force to Jack up a Truck's rear tyres

Hi, I previously posted about the statically indeterminate truck problem. Thank you to everyone who helped me. However, I now realised that isn't the problem I need to solve. I need to know the force of the linear actuators to lift the rear tyres off the ground. Since the tyres will be...
10. ### B What force will be felt by ##B## when a rod is rotated?

We have a rod ##AB## of mass ##m##, a force (perpendicular to AB) is applied at ##A##. I want to know how much force will ##B## going to feel? When ##F_1## is applied at ##A## rod will rotate about its COM (which lies at the Center) and hence the point ##B## will also move (a little downwards...
11. ### Confusion on the concept of point of rotation

--no explanation as conceptual error--
12. ### Mathematically Modeling a Rolling Body with Slipping

Basically, I want to know if my assumptions and workings are correct. This is how I see this situation. First, I'm viewing this body as a series of disconnected points, like I have in this animation I made, modeling purely rolling motion. Modeling the body like that worked in that case, and...
13. ### Finding the angular acceleration of a flywheel

I have solved part a using the conservation of energy, getting a (correct) answer of 47.9 km/h, but I am unable to make headway with part b. Based on the flywheel rotating at 237rev/s when the car is moving at 86.5 km/h, I obtained omega = (237*2pi)v/24=62v. Differentiating both sides should...
14. ### Man rotating in a merry-go-round and grabbing a pendulum

Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) ##r'##, ##v'## and ##a'## are the position, velocity and acceleration vectors, all relative to...
15. ### Rotational and translational motion

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...
16. ### Rotating pendulum

is this eqn correct
17. ### Determine the acceleration of the cylinder axis if there is no slip

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...
18. ### Find the acceleration and the work done by a force pulling a spool?

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...
19. ### Rotational Movement of a Disc

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...
20. ### Friction between two disks

Homework Statement This problem was originally posted on Physics Problems Q&A: http://physics.qandaexchange.com/?qa=616/friction-between-two-disks Homework Equations Second Newton's law for rotation: $$\tau = I \alpha = RF$$ The Attempt at a Solution I tried to solve this problem as...
21. ### Cylinder lying on conveyor belt

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##, mass...
22. ### Frictional force between two rotating cylinders

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 making...
23. ### Cylinder rolling on a moving board

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 roll...
24. ### Torque exerted by a flywheel

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 velocity...
25. ### Angular velocity equation

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 a...
26. ### Questions: Spherical habitat

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...
27. ### Rotational momentum

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 2.0...
28. ### B How long would it take to stop the rotation of the Earth?

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...
29. ### Experimental determination of the moment inertia of a sphere

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...
30. ### I Free Precession animation - body frame to space frame

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...