A disk is initially rotating counterclockwise around a fixed axis with angular speed w0. Answer the questions below. A. What is the net torque acting on the disk if the radius is 0.6 m? B. If the moment of inertia of the disk is 4kg ∙ m^2, what is the angular acceleration of the disk? C. If the initial angular velocity is 6 rad/s counterclockwise, what is the angular velocity after 10 seconds? D. What happens to the angular velocity of the disk over time? Sketch a graph!

You and your friend ride a merry-go round. You sit further away from center (2r) but your friend sits closer to the center (r). If the angular speed of the system is a constant, what can you say about following for you and your friend?a. linear speed? b. Angular speed?c. radial acceleration?b. tangential acceleration? 2c. if the ride starts with zero angular speed and run with constant angular acceleration of 2.00 rad/sradius 4m circle., calculate final angular displacement and linear displacement you and your friend travel?

A torque of 55 N·m producing a counterclockwise rotation is applied to a wheel about its axle. A frictional torque of 7 N·m acts at the axle. a. What is the net torque about the axle of the wheel? b. If the wheel is observed to accelerate at the rate of 4 rad/s 2 under the influence of these torques, what is the rotational inertia of the wheel?

After fixing a flat tire on a bicycle you give the wheel a spin. Its initial angular speed was 5.40 rad/srad/s and it rotated 15.9 revolutions before coming to rest. You may want to review (Pages 305 - 307) . Part A What was its average angular acceleration? Express your answer using three significant figures. Part B For what length of time did the wheel rotate? Express your answer using three significant figures.

2. A yo-yo consists of two solid disks, each of mass M and radius 3R. The two disks are connected by a rod of radius R and negligible mass. Assume the yo-yo starts at rest. a. Use the view on the right to draw the extended free body 3R diagram for the yo-yo. b. What is the moment of inertia of the yo-yo about an axis through its symmetry axis? м м c. Write Newton's 2nd law for the yo-yo. Choose your coordinate system carefully. d. Write the rotational form of Newton's 2nd law for the yo-yo. Treat the center of mass as being at the axis of rotation. Choose the positive direction of the rotation so a is positive. e. The point where the yoyo is momentarily at rest is where the string contacts the rod of the yo-yo. Use this to obtain a relation between the acceleration of the center of mass and the angular acceleration. f. Determine the linear acceleration of the yo-yo.

3. A telephone pole has been knocked over by the wind so that it makes an angle of 0 with the vertical. The wind has stopped blowing and the pole is to be cut down as shown. nail L cut Once the cut is across most of the thickness of the pole, the pole begins to tip over. As the pole tips, the bottom of the pole stays attached to the base by the remaining part of the pole that was not cut (but the torque from the base on the tipping pole is negligible). There is a nail (of negligible mass) on the pole located a distance x. The length of the pole from the cut to the top is L. Remember that the moment of inertia of a stick of mass m and length L about its end is mL?.

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Suppose the rotational kinetic energy of a solid disk is 1000 J when the disk has an angular velocity of 3 rad/s. What is the disk's moment of inertia? If the mass of the disk is 50 kg, what must be its radius? moment of inertia: A. 276.5 kg-m? B. 222.2 kg-m? D. 238.5 kg-m? E. 239.2 kg-m? С. 175.9 kg-m? F. 170.3 kg-m? /--/ radius: А. 2.490 m D. 2.536 m В. 2.981 m Е. 3.341 m С. 3.212 m F. 3.195 m

For a solid disk, I= 1⁄2 mr?. If a solid disk of mass=5.0 kg has a radius of .25 m has force of 12 N exerted at the rim: (Remember significant digits.) a.) What is the angular moment of inertia (I)? kgm2 b.) What is the magnitude of the torque exerted? Nm c.) What is the magnitude of the angular acceleration of the disk? rad/s?

A metal disc in a playground with a mass of 45 kg and a diameter of 4 meters is rotating on its central frictionless axis with an initial angular velocity of 3 rad/s. A child with a mass of 14 kg suddenly jumps unto the disc and stands on the edge. a.What is the new angular velocity of the disc with the kid on it? b. What is the tangential velocity of the kid as he rides the disc?

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The force of F = (2i -5j) N is acting on a particle whose position vector is r = (i +0.5j +2k) m Calculate the torque vector about the origin in Nm (Hint: consider the vector product) a. 8 b. 10i +4j - 6k c. 2i-2.5J d. (-1k) e. O f. (k) Nm 2i -2.5j +2k

Masses M = 6.0 kg and m = 3.0 kg are connected by a massless rope as shown in the figure below. The pulley has radius 30 cm. Assume the pulley is a solid cylinder with moment of inertia I =(1/2)MpR2 and that Mp = 42 kg. i. What is the angular momentum of the system in terms of the speed (v) of the two blocks? ii. What is the net torque on the system? iii. Use dL/dt = τext to find the acceleration (a).