A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.

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60 views

Why doesn't the string slack in the motion in a vertical circle even if tension is zero?

Suppose a particle of mass $m$ is attached to an inextensible string of length $R$ and is undergoing vertical - circular motion. The centripetal force is given by the tension & its weight: $$T ...
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1answer
40 views

Angular velocity formula for a particle?

I know that when the motion of a particle is circular about the origin then: $$\vec v=\vec \omega \times \vec r$$ But that this does not hold for any motion with a radial as well as tangential ...
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3answers
124 views

Torque on a disc?

In the following diagram: Point(c) is a going into the page and attached to the disc, Point(c) applies a torque($\tau$) to the disc, and it starts to rotate due to that torque. And if point(c) was ...
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1answer
113 views

Finding time period of oscillations in a multiple spring system attached to a solid cylinder [closed]

A solid cylinder of mass $m$ and radius $R$ is kept in equilibrium on horizontal rough surface. Three unstretched springs of spring constant $k$, $2k$, $3k$ are attached to cylinder as shown in the ...
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1answer
53 views

Rotational Equilibrium Problem [closed]

The question is as follows: One end of a uniform 4.0-m rod, whose weight is w, is supported by a cable that makes an angle of 37° with the horizontal. The other end of the bar rests against a wall ...
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2answers
100 views

How to determinate the minimum period of oscillation for a physical pendulum? [closed]

A physical pendulum consists of a thin homogeneous rod of length $l$, suspended by a point $O$ at a distance $x$ from the center of gravity ($x<\frac{l}{2}$), oscillating in a vertical plane. ...
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1answer
49 views

How much energy would it take to stop Earth's rotation on its axis?

I see a lot of questions regarding situations what would happen if the world would stop spinning. This got me to wondering how much energy it would actually take to stop the world from spinning.
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3answers
85 views

Newton's Second law of Rotation

In my book (Halliday Resnick Walker) there is a solved example which is as follows There is a uniform disk with mass $M$ = 2.5kg and radius $R$ = 20cm, mounted on a fixed horizontal axle. A block ...
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1answer
38 views

Rotational dynamics about a point or an axis?

In several books and sites, its written that torque is calculated about an axis and angular momentum is calculated about a point. In MIT's Angular momentum lecture pdf, Angular momentum has been ...
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1answer
126 views

What forces cause the centripetal acceleration in circular motion on a merry-go-round?

Suppose you stand on a merry-go-round spinning at $f$ revolutions per second and you are $R$ meters from the center. What forces act on you? If you were tied to a rope like in Fig 2 you would follow ...
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1answer
272 views

Can a ball stay still while laying on a inclined plane?

Suppose there is a ball on an inclined plane. So, there are three forces acting on it: normal force from the plane, gravity (which can be decomposed in the component of gravity perpendicular to the ...
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1answer
385 views

Model the gyroscopic effect for 3axes stabilisation

Context I am trying to stabilise a platform on a guimbal using 3 axes gyroscopes. I have made tons of research (same problem for weeks even months now) without being able to properly model the 3 ...
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1answer
72 views

Will it start rolling?

Suppose you have a wheel standing stationary on a rough horizontal surface. Now you apply a horizontal force at the top of the wheel. Now, will the wheel experience any force or will it just start ...
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1answer
55 views

If the axis of rotation is fixed, is it ok to say clockwise torque?

I know that the direction of torque is along the axis of rotation, but would it be acceptable to say, for example considering a vertical thin rod in the x-y plane with a force acting on the bottom end ...
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2answers
259 views

Inertia matrix of a rod rotating about an axis [closed]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
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1answer
55 views

Linear speed of falling pencil [closed]

Find the final linear speed of pencil. Pencil would move because of gravity. Let's assume that it is balancing on the tip. We do not take friction into consideration. – Given $$d=0.15m$$ Similar ...
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1answer
77 views

Finding acceleration using rotational dynamics [closed]

I'm asked to find the linear acceleration of this object for a given tension $T$ knowing that both discs have mass $M$ and we don't consider the mass of the bar. The answer of the book is ...
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1answer
160 views

Purely mechanical description of how gravity causes a gyroscope to precess

I know the vector equation that relates torque to moment of inertia and angular momentum. What I want to know is what physical mechanisms actually occur to keep the gyroscope from falling. Where is ...
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1answer
276 views

Contradiction regarding friction of a rolling cylinder in an inclined plane

I came upon this while wondering whether the friction of a rolling cylinder on an inclined plane depends on the value of friction coefficient. now, $$f\leqq\upsilon N$$ Again after calculating I ...
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1answer
216 views

Rotation of bodies about centre of mass [closed]

Imagine two masses connected by a massless, inextensible string kept on a smooth, horizontal plane. Now suppose one of the masses is given a velocity perpendicular to the string. So the masses will ...
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1answer
350 views

Centrifugal force acting on ring [closed]

Take for example the case of a rod rotating about an axis passing through its centre of mass and perpendicular to it. It has a ring hung from one of its sides. The rotation of the rod causes the ring ...
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1answer
502 views

Will a free-falling rod (without drag) rotate?

When we consider a bicycle is turning on a flat plane, we know that there is friction, which provide centripetal force on the bicycle. And we know that the bicycle is no longer perpendicular to the ...
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3answers
509 views

Does the Earth spin because its surface has less mass than its core as lighter things travel faster in space?

Would heavy elements from space hitting the Earth slow down the earth's rotation as the difference between the masses of the core and surface would be less?
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2answers
5k views

Center of a mass of a hemisphere [closed]

How can I show that position vector of the center of a mass of a hemisphere is $(0,0,\frac{3a}{8})$ where $a$ is radius of a hemisphere, $x$ and $y$ axis are laying on the base and $z$-axis is ...
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1answer
81 views

Why do cosmic bodies revolve? [duplicate]

Why do cosmic bodies such as planets, stars, satellites revolve? What made them to revolve after the formation of universe?
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2answers
4k views

DC Motor Torque Constant

I am very new to DC motors and to stackexchange. Please correct me if anything I said does not make sense. For DC motors, the equation looks like this: $P = \tau\dot{\theta}$ where $P$ is power, ...
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1answer
1k views

Finding Rotational Kinetic Energy Of A Clock

The problem I am working on is: Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure ...
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2answers
681 views

Setting up equations for a Rotational Kinematics system

I'm having a hard time setting up equations for the following problem: A green hoop with mass $m_h$ and radius $r_h$ m hangs from a string that goes over a blue solid disk pulley with mass $m_d$ ...
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3answers
13k views

Finding Angular Acceleration of rod given radius and angle

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular ...
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2answers
565 views

Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
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1answer
127 views

Period of an Object in Periodic Motion

My attempt (if it matters): The initial period is given by $T_X = \frac{2\pi X}{v}$ for some $v$. The new period is given by $T_Y = \frac{2\pi Y}{v}$ for the same $v$. $Y = \frac{X}{2}$, so ...
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2answers
6k views

Rotational kinetic energy during vertical circular motion of a particle

Why is it not necessary to take into account rotational kinetic energy when using the Law of Conservation of Mechanical Energy to solve vertical circular motion problems? After all, the particle is ...
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1answer
284 views

Relationship between the “angle of the floor” and the angular velocity in a banked turn?

Wel, imagine that you're in a carousel, and the floor is, let's say at $\theta=0$ so it's totally horizontal, if $\theta=90$ the floor would be vertically. The object put above the floordoesn't move ...
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1answer
402 views

Angular velocity $\omega$ by $v$

We have two girls, with mass ($M$). They become close to each other in speed of $V$. The distance between them is $3L$. I was asked to calculate the Angular velocity ($\omega$) of the two girls. So ...
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1answer
265 views

What causes a gyroscope to eventually rotate/fall over?

Hey so I've just learned about angular velocity and momentum and how torque changes it. Looking at a wheel spinning around an axis, with one end being held up by a rope, what causes the wheel to ...
0
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1answer
17 views

If the velocity of an object, rotating on a vertical circle, at the topmost point is zero, how can it loop the whole circle?

Normally, if a body is attached to a string & is rotated in a vertical circle, then to loop the whole circle, the rope must not slack at the topmost point & there should be a velocity for ...
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1answer
27 views

Spinning Ball in Frictionless Tube

If we have a ball in a frictionless tube, and we begin to spin the tube about one end, the ball will exit the tube, correct? Indeed, there must be some centripetal acceleration, but then what force is ...
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1answer
36 views

Cancelling internal forces/moments term when deriving inertial matrix

I am attempting to derive the inertial matrix for a general rigid body of mass $m$ as shown in the following diagram: The green vectors indicate the key position vectors: Position of centroid ...
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2answers
32 views

When I change the rpm of a turntable, how long does the turntable to get to the new rpm?

If the turntable was rotating at 16 rpm and I switched it to 30 rpm, is the change in speed pretty much instantaneous, or is their a period of acceleration? When I did it, the change appeared to be ...
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3answers
73 views

Maximum acceleration for a vehicle [closed]

I'm in engineering school and we have a project: we have to build a amphibioues vehicle; I'm looking for a formula. Our vehicle has to go as far as possible with its unique source of energy, a ...
0
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1answer
55 views

How the torque/moment-of-force can be mathematically defined?

Given the definition of torque/moment-of-force $\mathbf F$ applied in $P$ with respect to the pole $O$ $$ \mathbf M_O=\vec{OP}\times\mathbf F $$ and given that the vectors $\vec{OP}$ and $\mathbf F$ ...
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2answers
133 views

When does the 'standard' angular velocity formula not hold?

I have read that the formula for angular velocity: $$\dot {\vec r}=\vec \omega \times\vec r \tag{1}$$ does not hold in some situations, but the book does not specify what situation so please could you ...
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1answer
61 views

Finding the centripetal force at any random point in a wheel which is rotating as well as translating

If we have a wheel which is decelerating due to friction with acceleration $-A$ and angular acceleration $-\alpha$, and we want to find the acceleration at any point, then we can simply find it using ...
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1answer
47 views

How to calculate time from different instantaneous velocities and accelerations?

I have a closing door, that moves from angle 75 to angle 5. Torque acting on that door at each angle is known -of course differs at each angle- I want to calculate the time required for that door to ...
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2answers
211 views

Is work done in rolling friction?

I am confused by rolling friction. Suppose you have a cylinder rolling which starts at rest at the top of an incline plane and begins to roll down the plane without slipping. Is work done by the ...
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3answers
121 views

Rotational Inertia of a Disc and Subsequent Acceleration

This is more of a conceptual problem as opposed to anything wrong with the maths! (I think/I hope! :) ) But essentially the problem states: imagine a circular flat disc of radius $R$ and of mass ...
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1answer
41 views

Transmissibility

An extract from a school maths mechanics textbook reads: To deal with cases in which the body is not rotating freely under gravity, we need to take into account also the work done by other ...
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1answer
43 views

An unwinding cable problem [closed]

Suppose a light cable is wrapped around a solid cylinder with mass $M$ and radius $R$. The cylinder rotates with no friction about a stationary horizontal axis. The free end of the cable is attached ...
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1answer
32 views

When conserving angular momentum, about which point(s) should it be calculated?

In my physics problem I have a ball fired at a non fixed bar, which is moving at some velocity, causing them both to stick together and the bar-ball pair to rotate about the new center of mass. About ...
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1answer
532 views

The direction of frictional force in smooth rolling motion

I want to ask about the direction of frictional force in smooth rolling motion which means the rolling object doesn't slide on the surface. Here is the first case, the wheel rolls to the right so the ...