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At what $ω$ would the dust particles fly off the tilted rotating disc?

Yes, your analysis is correct. The equation is indeed: $$μmgcosθ=[(m²g²sin²θ + m²ω⁴x²+ 2(mgsinθ)(mω²x)cosΦ)]^.5 (1)$$ Since $θ$ is small you can approximate the equation to be $$μmg=(m²ω⁴x²)^.5$$ ...
Piyush Lath's user avatar
1 vote

Conversion of linear velocity to angular velocity and vice versa

Dynamics The object of mass $m$, and mass movement of inertia (sphere) of ${\rm I} = \tfrac{2}{5} m R^2$ has the following momentum values $$\begin{aligned} \vec{p} & = m \vec{v} & & \text{...
John Alexiou's user avatar
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Is this how friction is a centripetal force when a car is making a turn?

A non-accelerating wheel is able to roll with minimal force. So in the ideal case that a car is moving at a constant speed without braking or acceleration from the transmission, the wheel exerts ...
BowlOfRed's user avatar
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Is this how friction is a centripetal force when a car is making a turn?

my intuition would not lead me to believe it would act perpendicular to velocity I'm not sure, but I can guess that your intuition is what is leading you astray. Because we first learn about kinetic ...
Ben H's user avatar
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1 vote
Accepted

Friction behaviour for a mass in contact with a surface

In the Coulomb model of friction, the maximum static friction force is proportional to the applied load $N$ and independent of the surface area in contact. Thus $F_{friction} \le \mu N$ where $\mu$ is ...
gandalf61's user avatar
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How can I easily structure harmonic motion in a forces problem?

Your problem is describing a damped harmonic oscillator. The force of magnitude $8Mx$ is just Hook's law. The reason for the negative sign is that it always points in the direction needed to restore ...
user256872's user avatar
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1 vote

Role of the friction force in rolling without slipping

To demonstrate how an apparent clockwise torque on an wheel going to the right does not necessarily cause an acceleration to the right, consider the following thought experiment. In the diagram A and ...
KDP's user avatar
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Role of the friction force in rolling without slipping

Let's assume a wheel is rolling without slipping across a horizontal surface. If it moves with a constant velocity, then the angular velocity, $\omega$, is also constant and therefore both the net ...
Ben H's user avatar
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Role of the friction force in rolling without slipping

The force of friction opposes the direction of acceleration. For a wheel, the point of contact at any given moment in time is not moving w.r.t the surface. If you like, the point is "stationary&...
Obliv's user avatar
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When not pedaling, the friction force on the wheels of the bicycle is directed backwards, but doesn't this give the tires angular velocity?

It is not friction at the contact point of the wheel that slows the wheel down and the friction does not give the wheel angular velocity. The main cause of the slowing down is due to the hysteresis of ...
KDP's user avatar
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1 vote

Friction force variable or non-variable force

In the ideal world, the coefficient of kinetic friction is constant. In the real world, the coefficient of kinetic friction varies with the relative velocity of the surfaces.
Chet Miller's user avatar
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0 votes
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Friction force variable or non-variable force

Whenever a two bodies undergo relative motion, they pull each other with kinetic friction, i.e F = (kinetic friction coefficient)(normal force) When two bodies have the tendency to undergo relative ...
Jyot's user avatar
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Does Accelerating to Double the Speed Require Quadruple the Fuel Consumption, or Double the Fuel Consumption?

Work done (which is a measure of energy input) has the formula $(F \ d)$ where F is force and d is the displacement or distance travelled. Distance travelled in time t with acceleration a is $d = 1/2 ...
KDP's user avatar
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0 votes

Is force really considered a push or a pull?

Consider two cars, A and B, that have bumpers mounted on springs for cushioning shocks. Now if car A with its engine on pushes car B (engine off and free-wheeling) along at a constant 70 mph then ...
KDP's user avatar
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Why does critical damping return to equilibrium faster than overdamping?

WLOG you can rescale x so that the initial displacement is 1 and rescale time so that $\omega _0 = 1$. For convenience you may also relabel $\gamma = 2q$ which is fine because we will check our result ...
Harvey Williams's user avatar
0 votes

How do I calculate frictional forces of an object sliding laterally on a sloped plane?

For some arbitrary motion we can separate the instantaneous velocity of its motion into components across and down the surface of the wedge, the x and y directions in the figure. Likewise the kinetic ...
Bob D's user avatar
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1 vote

Maximum no. of books that can be held between two hands without the books falling down?

If the books are in equilibrium the net horizontal force on each book must be zero. Since the hands exert a horizontal force of $120$ N on the two outer books then each book experiences a force of $...
gandalf61's user avatar
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0 votes

How do I calculate frictional forces of an object sliding laterally on a sloped plane?

Under the simple kinetic friction model, $\mu_k N$ is the strength of the friction force, full stop, independent of the direction of motion. Then, the direction of the kinetic friction opposes the ...
march's user avatar
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0 votes

Acting forces on a curve ball (billiards)

The poster is correct that the ball would normally veer to the right with the left-side hit causing clockwise rotation. This is not a regular hit on ball on the left side of cue ball, however. This ...
Paul Bell's user avatar
7 votes

Can the value of Limiting friction be achieved?

Technically, from $$ma = F_{inp} - \mu_sN $$ follows that for body to have $a \gt 0$, it must be true $F_{inp} \gt \mu_sN$. So you need to slightly overcome static friction for body to move. ...
Agnius Vasiliauskas's user avatar
8 votes
Accepted

Can the value of Limiting friction be achieved?

My teacher states that if we apply an external force just equal to the value of limiting friction, then the body will start moving We generally say that when the applied force equals the limiting ...
Bob D's user avatar
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1 vote

Acceleration of a point

This is a 2-degree of freedom system, with two equations of motion, one for each mass. The motion of point P is kinematically constrained to the 2 DOF, such that if you figure out how much each mass ...
John Alexiou's user avatar
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0 votes

Acceleration of a point

I think I understand the source of confusion: you've read "acceleration at point" as if it were jargon, a term with a special meaning. It's not: there is nothing special about this point ...
kkm -still wary of SE promises's user avatar
3 votes

Acceleration of a point

The diagram is not completely clear, but I think it is meant to convey that there is a fixed length of string/rope that goes around the two pulleys, with one end at $P$ and the other end attached to ...
gandalf61's user avatar
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1 vote

Hasn't the direction of Tension force been considered wrong here?

The free body diagrams tell us that for equilibrium the rod is in compression, not tension, in order to resist the horizontal components of the normal force of the wall and the friction force of the ...
Bob D's user avatar
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2 votes

Hasn't the direction of Tension force been considered wrong here?

Tension is typically used to describe a pulling force in scenarios with cables or ropes. In such cases, tension can only pull along the length of the rope, but not push. This problem uses a rigid rod ...
Nuclear Hoagie's user avatar
4 votes
Accepted

Hasn't the direction of Tension force been considered wrong here?

The rod is in a state of compression not tension.
mike stone's user avatar
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0 votes

Why do ball bearings work?

It is a good description. I would add that if the ball were between two plane surfaces, the relative velocity $v$ between them would determine the angular velocity of the ball with radius $r$: $r\...
Claudio Saspinski's user avatar
2 votes
Accepted

Why do ball bearings work?

Yes, it is. Let's have a closer look. Because (as you point out) you can make the coefficient of rolling friction practically as small as you want, and geometrically enforce the no-slip condition by ...
niels nielsen's user avatar
0 votes

Is both spring force and friction force are equal in this problem?

If the spring is at rest, you can say $f_{sp1} + f_{sp1} = kx$. One more thing is $N_1 = N_2$ and hence, $f_{sp1} = f_{sp1}$.
Dev Not Taken's user avatar
0 votes
Accepted

Is both spring force and friction force are equal in this problem?

Yes. If the end of the spring is not moving then the spring force is equal and opposite to the sum of the frictional forces.
gandalf61's user avatar
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1 vote

Accelerating car under the influence of rolling friction

I've already accepted user256872's answer, but I just wanted to add some remarks to point out the flaws in my initial reasoning. Conventions about frictional forces Namely, my troubles seem to mostly ...
BlenderBender's user avatar
1 vote
Accepted

Accelerating car under the influence of rolling friction

The idea of rolling friction is fundamentally a macroscopic, experimental observation, which states that the work is $dw=\mu_R m\vec g\cdot d\vec s$. As for your questions, The dissipational energy ...
user256872's user avatar
  • 6,601
1 vote
Accepted

Why the orientation of an object on Earth rotates with the rotation of earth? Is this due to friction?

So people who start to drive cars notice something interesting about the brake pedal: it “pitches you forward.” And this makes your passengers a little bit sick if you don't do it carefully. The ...
CR Drost's user avatar
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1 vote

When not pedaling, the friction force on the wheels of the bicycle is directed backwards, but doesn't this give the tires angular velocity?

When we are pedaling, a torque $\tau$ is induced in the wheels of the cycle. Since the tires generally have a good traction with the road, the friction force acting on the cycle would be $f_1 = \frac{\...
Dev Not Taken's user avatar
3 votes

When not pedaling, the friction force on the wheels of the bicycle is directed backwards, but doesn't this give the tires angular velocity?

Practically there is not just point of contact between the tyres and the road but rather an area of contact which is due to the deformation of the tyres. Due to this deformation the normal force acts ...
Aarush Saharan's user avatar

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