Physics for Scientist and Engineers third edition Rotational Motion About a Fixed Axis Problems

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1 A particular bird s eye can just distinguish objects that subtend an angle no smaller than about 3 E -4 rad, A) How many degrees is this B) How small an object can the bird just distinguish when flying at a height of 100 m Answer: 0.017, 3 cm RoessBoss 1

2 The platter of the hard disk of a computer rotates at 5400 rpm A) What is the angular velocity of the disk A) what is the angular velocity of the disk B) If the reading heat of the drive is located 3.0 cm from the rotation axis, what is the speed of the disk below it? C) What is the linear acceleration of this point D) if a single bit requires 5.0 µm of length along the motion direction, how many bits per second can the writing head write when it is 3.0 cm from the axis? E)If the disk took 3.6 s to spin up to 5400 rpm from rest, what was the average acceleration Answer: 570 rad/s; 17 m/s; 9700 m/s^2; 3.4 E 6 bits per second; 160 rad/s^2 RoessBoss 2

3 Through how many revolutions did the hard drive of the previous example turn to reach 5400 rpm during its acceleration period? Assume constant angular accleration Answer: 1.04 E 3 rad, 165 rev RoessBoss 3

4 A bicycle slows down uniformly from V0= 8.40 m/s to rest over a distance of 115 m. Each wheel and tire has an overall diameter of 68.0 cm. Determine A) the angular velocity of the wheels at the initial instant (t=0) B) the total number of revolutions each wheel rotates before coming to rest C) the angular acceleration of the wheel D) the time it took to come to a stop Answer: 24.7 rad/s; 53.8 rev; rad/s^2; 27.4 s RoessBoss 4

5 Two thin cylindrical wheels of radii R1= 30 cm and R2= 50 cm are attached to each other on an axle that passes through the center of each. Calculate the net torque on the two wheel system due to the two forces shown, each of magnitude 50 N Answer:-6.7 m N RoessBoss 5

6 Two small weights of mass 5.0 kg and 7.0 kg are mounted 4.0 cm apart on a light rod (whose mass can be ignored). Calculate the moment of inertia in the system A) when rotated about an axis halfway between the weights B) when the system rotates about an axis 0.50 m to the left of the 5.0 kg mass Answer: 48 kg m^2; 143 kg m^2 RoessBoss 6

7 A 15.0 N force is applied to a cord wrapped around a pulley of Mass = 4.00 kg and radius= 33.0 cm. The pulley is observed to accelerate uniformly from rest to reach an angular speed of 30.0 rad/s in 3.00 s. If there is a frictional torque (at the axle)= 1.10 m N, determine the moment of inertia of the pulley. The pulley is assumed to rotate about its center Answer: 3.85 m N; 10.0 rad/s^2; kg m^2 RoessBoss 7

8 Consider again the pulley from the previous problem. This time suppose that instead a constant 15.0 N force being exerted on the cord, we now have a bucket of weight 15.0 N hanging from the cord, which we assume not to stretch or slip on the pulley. A) calculate the angular acceleration of the pulley and the linear acceleration of the bucket B) Determine the angular velocity of the pulley and the linear velocity of the bucket at t=3.00 s if the pulley (and bucket) start from rest at t=0 Answer: 6.98 rad/s^2; 2.30 m/s^2; 20.9 rad/s; 6.91 m/s RoessBoss 8

9 Suppose a 60 kg person stands on the edge of a 6.0 m diameter circular platform, which is mounted on frictionless bearings and has a moment of inertia of 1800 kg m^2. The platform is at rest initially, but when the person begins running at a speed of 4.2 m/s around its edge, the platform begins to rotate in the opposite direction. Calculate the angular velocity of the platform Answer: 0.42 rad/s RoessBoss 9

10 Flywheels are simply large rotating disks, have been suggested as a means of storing energy for solar powered generating systems. Estimate the kinetic energy that can be stored in a 20,000 kg (10 ton) flywheel with a diameter of 20 m. Assume it could hold together at 100 rpm Answer: 10.5 rad/s; 5.2 E 6 J; 3.6 E J RoessBoss 10

11 A rod of mass M is pivoted on a frictionless hinge at one end. The rod is held at rest horizontally and then released. Determine the angular velocity of the rod when it reaches the vertical position, and the speed of the rod s tip at this moment Answer: RoessBoss 11

12 What will be the speed of a solid sphere of mass M and radius R0 when it reaches the bottom of an incline if it starts from rest at a vertical height H and rolls without slipping? Ignore losses due to dissipative forces, and compare your result to that of an object sliding down a frictionless incline. Answer: RoessBoss 12

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