# Problems in Classical Mechanics Involving Rotation

Please see attachments for details.

11. The angular speed of a wheel increases at a constant rate of 1.5 rad/s2. During a certain 3.2 s time interval, it makes four complete revolutions. If the wheel started from rest, how long has it been in motion at the start of this time interval?

12. An airplane makes a circular turn of radius 9.0 km at a constant speed of 650 km/h. Calculate the magnitudes of the plane's

a)angular velocity

b)centripetal acceleration

c)angular acceleration

d)tangential acceleration

13. A square plate has a side length of 1.2 m. An applied torque of 300 NÃ??Ã?·m gives the plate an angular acceleration of 4.8 rad/s2 about an axis through the centre of the plate. Determine the plate's mass.

14.A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s.

a)Draw free-body diagrams for the block and the cylinder.

b)Calculate the tension in the string.

c)Calculate the mass of the cylinder.

15.

solid sphere of mass 6.0 kg is mounted on a vertical axis and can rotate freely without friction. A massless cord is wrapped around the middle of the sphere and passes over a 1.0 kg pulley and is attached to block of mass 4.0 kg, as shown. What is the speed of the block after it has fallen 80 cm? Treat the pulley as solid cylinder.

16. Consider a uniform rod of mass 12 kg and length l.0 m. At its end, the rod is attached to a fixed, friction-free pivot. Initially the rod is balanced vertically above the pivot and begins to fall (from rest) as shown in the diagram. Determine,

a) the angular acceleration of the rod as it passes through the horizontal at B.

b) the angular speed of the rod as it passes through the vertical at C.

17.A uniform vertical beam of mass 40 kg is acted on by a horizontal force of 520 N at its top and is held, in the vertical position, by a cable as shown.

Draw a free-body diagram for the beam, clearly labeling all of the forces acting on it.

a)Calculate the tension in the cable?

b)Determine the reaction forces acting on the beam by the ground?

18

A 30 kg neon sign is suspended by two cables, as shown. Three neighborhood cats (5.0 kg each) find the sign a comfortable place. Calculate the tension in each cable when the cats are in the positions shown.

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#### Solution Summary

We solve various problems in classical mechanics involving rotation, force, and torque.

Physics Problem - A uniform, hollow, cylindrical spool

Please help with the following classical mechanics problem. See attached file for full problem description.

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A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R and mass M as in the attached .jpg. It is mounted so that it rotates on a fixed horizontal axle. A counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls from rest at t = 0 to a position of y at time t. Show that the torque due to the friction forces between spool and axle is Tf= R { m [ g - (2y / t^2)] - M (5y / 4t^2)}

Please see the attached file for an accompanying illustration.

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