# Tag Info

### Confusion about the Spinning Top

I think your equation $\Omega\wedge P_c=r_c\wedge Mg$ is not correct. The l.h.s. should be the derivative of the total angular momentum w.r.t. to point of contact with the floor, not w.r.t. the center ...

### Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples?

An astronaut sits in a rocket on the launch pad. The rocket is launched. From the astronaut's point of view, the rocket is stationary. A time dependent fictitious force sprang into being and pushed ...

### Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples?

The Coriolis effect arises when you use co-ordinates fixed in an accelerating frame of reference (in this case, the surface of a rotating planet). If you use co-ordinates fixed in a frame of reference ...

### Physical intuition about the inertia tensor

I have also encountered the same problem until recently I understood the meaning behind the indices. Although there are a lot of definitions of a tensor, we are left to decide which one is palatable ...
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### Faster Small Tires vs Slower Large Tires

Long distance trucks use large tires in part because of rolling resistance, as @AgniusVasiliauskas pointed out. But also a large tire has a more gentle curvature. This means a larger contact patch. ...
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### When to apply $I_c \underline{\omega} = \underline{M_c}$?

The expression $\underline{M}_c = \mathrm{I}_c \,\underline{\omega}$ is never correct. I think you forgot the time derivative of rotational velocity here. Also, the are Coriolis torques that relate ...
1 vote

### Acceleration calculation for an object with is rotating about it's COM and it's COM is revolving about another object

In the frame of the satellite, the acceleration of A is just acceleration from rotation around the satellite. In the frame planet, it's the sum of the accelerations of A wrt the satellite plus the ...
1 vote

### Spinning top fixed point

When calculating rotation problems, with torques and suchlike, it is necessary to choose an origin for the coordinate system. This choice is ultimately arbitrary since the equation of motions are ...

### Why do we talk about inertia tensor?

A rank 2 tensor is something that relates two vectors. In this case, the MMOI tensor relates the rotational velocity vector to the angular momentum vector. Given a solid whose internal particles are ...

### Why do we talk about inertia tensor?

The moment of inertia you mentioned is only for a single, given axis of rotation. It's used to compute the angular momentum related to his axis: $$L=I\omega$$ If you want to generalize the result in ...
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### What does inextensible string mean and how can that be applied in real life

It sounds like you have the right understanding of inextensible. All real strings (ropes, cables, chains etc.) will stretch to a certain degree when under tension so describing a string inextensible ...

### Can the value of friction force ever exceed value of applied force?

First, there is an important qualification to "the value of friction force can never be greater than the applied force". This refers to static friction. Indeed, you pose a scenario where &...

### Can the value of friction force ever exceed value of applied force?

To answer the question in the title, the friction force can be larger than the normal force that is producing it. There is no restriction. Coefficients of friction larger than 1 are not common in ...

### Can the value of friction force ever exceed value of applied force?

No. You've discovered the Class 2 Lever, which places the load between the input force and the fulcrum. You have correctly calculated that the friction force is 4 times the input force. The reason for ...
1 vote
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### Lagrangian Mechanics - Is the Given Answer Incorrect?

$\dot{\phi}$ is not a constant of the motion, so you can't treat it as constant when taking the derivative of $V_\text{eff}$ with respect to $\theta$. If you leave $V_\text{eff}$ in its original form,...

### What specifically about the torque vector is perpendicular? Is the torque vector like this only so that it works smoothly with linear algebra?

It's neither calculus nor linear algebra; rather, it's geometry, or perhaps representation theory, or Clifford algebra... each of which can lead to a long an in-depth answer. That will not be ...
1 vote

### Can the direction of angular momentum be changed without external torque?

In the absence of external torques with respect to a particular origin, the magnitude and direction of the angular momentum of a system are constant (with respect to that origin). So the most ...

### Rotating a lever — small end has more force but less speed?

There are two errors here. First, $F_{2} = F_{1}\frac{R}{r}$ is about the balancing of two torques in static equilibrium. That is, the usually case where this holds is where $F_1 R$ is one torque, ...
1 vote
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### Rotating a lever — small end has more force but less speed?

What accelerates object A is not the force $F_1$ that you applied to it, it's the net force that it experiences. $F_1$ is one component of the net force, but there is also a reaction force from the ...
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### How to know the direction of static friction with angular momentum?

In this case, the static friction is responsible for generating the circulation in the case of rolling without slipping. The reverse occurs when friction is a resistance to rolling. This is similar to ...

### Work Done on a rotating thin rod by hinge Forces

There is no friction so the only force on the rod at the hinge is the hinge reaction force. Is there a displacement of the hinge reaction force along the line of action of the hinge reaction force? As ...
1 vote

### Resisting Precession of a Gyroscope

I will first provide a link, and then I will go to your question specifically. For discussion of the underlying mechanics I refer to my 2012 answer: gyroscopic precession. (That discussion, ...

### Resisting Precession of a Gyroscope

Gravity provides a torque that would pull the gyro over if it is not spinning. When the gyro is spinning, in the non-inertial frame precessing with the gyro, fictitious forces are present. Consider ...

### Work done by static friction on a car

The answer by @stafusa is correct. The increase in kinetic energy (KE) of the car is due to the decrease in internal energy of the car (from combustion, batteries, etc.) This can be understood using ...
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### What is the general no slip condition for rotations?

Landau & Lifshitz explain an equivalent problem. Some observations: The Instataneous Axis of Rotation (IAR) is a straight line passing for the two poins of the disks, in contact with the flat ...
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### Seemingly correct and useful expression for kinetic energy of 3D rigid body not found anywhere

The expression you gave is very common. You mostly get if when going through the proof of König's theorem for a continous system, which involves going to the center-of-mass frame (hence getting the ...
The integral $$I= \int\mathrm dm\ r_\perp^2$$ is the moment of inertia about the given axis. You may be partway along the path to computing the moment of inertia tensor, which is useful describing ...
One thing that might give you better intuition is that the definition of an angle is the ratio of 2 lengths: $$\theta = \frac{s}{r}$$ With $s$ being the arc length traveled along a circle, and $r$ the ...