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vertical **rod** through a **horizontal** shaft of length a, as shown in **Fig**. 15.14(a). The wheel rolls without slipping about the Z axis with an angular velocity of Ω. φ.. a b c ^ρ ξ **P** y x O **P P** O x Z a R **Figure** 15.14 (a) Rolling motion of a cycle wheel connected **to a horizontal** shaft. (b) A view from the top. A line OP of the disk has rotated by.

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• No matter which **pivot** point you choose, an object that is not rotating is not rotating about that point. • For a rigid body in total equilibrium, there is no net torque about any point. • This is the basis of a problem-solving strategy.

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HRW **p**. 725 #55: **Figure** 29-46 in the text **shows** a rectangular, 20 turn coil of wire, 10 cm by 5.0 cm. It carries a current of 0.10 A and is hinged along one side. It is mounted in the xy plane, at an angle of 30 o to the direction of a uniform magnetic field of 0.50 T. Find the magnitude and direction of the torque acting on the coil about the hinge line.

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A uniform **horizontal** beam 8 m long is attached by a frictionless **pivot** to a wall. A cable making an angle of 37o, attached to the beam 5 m from the **pivot** point, supports the beam, which has a mass of 600 kg. The breaking point of the cable is 8000 N. A man of mass 95 kg walks out along the beam. How far can he walk before the cable breaks? T x.

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Three forces F1, F2 and F3 act on **a rod** at distances r1, r2, and r3 from the pivoted end, as shown in **fig**. 11.24a. Find the torque due to each force about the **pivot**. Solution: We adapt the convention that a torque tending to produce a counterclockwise rotation is positive (right-hand rule). 20 11.6 Rotational Dynamics of a Rigid Body (**Fixed**.

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**The figure above shows a rod that is fixed to a horizontal surface at pivot P**. The **rod** is initially rotating without friction in the counterclockwise direction. At time t, three forces of equal magnitude are applied to the **rod** as shown. Does the angular speed increase or decrease, and is the direction of rotation clockwise or counterclockwise?.

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**Figure** **shows** **a** light **rod** of length l rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the **rod** in **a** **horizontal** position. There is a **fixed** smooth ring at a depth h below the initial position of the hook and the hook gets into the ring as it reaches there. A box of mass m is initially at rest at the top of a.

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A uniform **rod** of mass 1.0 kg and length 2.0 m is free to rotate about one end (see the following **figure**). If the **rod** is released from rest at an angle of [latex]60^\circ[/latex] with respect to the **horizontal**, what is the speed of the tip of the **rod** as it passes the **horizontal** position?.

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networkx dfs example

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- 9 Problem 7 Given: A cylinder with an outer radius of R = 3 ft rolls without slipping on a
**horizontal****surface**.**The**center of the disk O has an acceleration that is known in terms of the position x of: ! a O= 3 2 x2 (x in feet and a O in ft/sec 2) At position 1 (x = 0), point O has a velocity of 1 ft/sec to the right. **Show**that if the center of mass is at a distance l from the vertex and m is the mass of the cone the**above**motion is only possible if . Determine the reaction at the support of the vertex . 38. A uniform heavy**rod**is held vertically by a**pivot**at its lower end and there is- 3. A pendulum is made from a rigid
**rod**of length L and mass M hanging from a frictionless**pivot**point, as shown below. The**rod**is released from a**horizontal**position. How does the (tangential) acceleration of the end of the**rod**at the moment of release compare to g? L 4. A wheel rotates with a constant angular acceleration α = 3.50rad/s2. - 5. There are two forces on the 2 kg box in the overhead view of the
**figure**below but only one is shown. The**figure**also**shows****the**acceleration of the box. Find the second force (**a**) in unit-vector notation and as (b) magnitude and (c) direction. 33 180 33 213 32 20.78 32 21 38.27 tan ( 32ˆ 20.78ˆ) 20.78 12 20 32 - A particle, of mass 10 kg , is suspended from the end B of the
**rod**. The**rod**is kept in a**horizontal**position by a light inextensible string BC, where C lies on the same wall vertically**above**A. In**the figure**, a 1.91 kg ball is connected by means of two massless strings, each of length L = 1.06 m, to a vertical, rotating**rod**.