CHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque

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1 7 1. Define Torque 2. State the conditions for equilibrium of rigid body (Hint: 2 conditions) 3. Define angular displacement 4. Define average angular velocity 5. Define instantaneous angular velocity 6. Define average angular acceleration 7. Define instantaneous angular acceleration 8. State four equations of rotational motion (Hint: Same as linear motion equations) 9. Define moment of inertia of a rigid body 10. State torque in term of moment of inertia 11. State rotational kinetic energy 7 P a g e

2 8 12. State work done for rotational motion 13. State power for rotational motion 14. Define angular momentum 15. State the principle of conservation of angular momentum 8 P a g e

3 9 1. A uniform rod pivoted at A is in equilibrium as shown in the figure. Determine a. the weight of the rod b. the normal reaction at the pivot Answer: (a) 10 N ; (b) 60 N 2. The figure shows a uniform rod of length 0.80 m and mass 0.50 kg resting on supports at end A and at point P, 0.20 m from end B. A load of 2.0 kg is placed at Q, 0.20 m from A. Determine the reaction at A and P. If another object is placed at B, determine the maximum mass of the object before the plank begins to tip. Answer: A = 14.7 N, P = 9.81 N ; m = 8.5 kg 3. Figure shows a metal rod, AB of weight, W = 400 N and length of cm that is hinged freely at end A. The rod is maintained horizontally by attaching a string at end B to the wall at point C. Point C is 60.0 cm vertically above point A. Determine a. the tension of the string b. the magnitude and direction of force at end A Answer: (a) 388 N ; (b) 388 N, 31.0º above positive x- axis 9 P a g e

4 10 4. A uniform ladder, AB of length 10 m and weight 50 N is resting against a smooth wall as shown in figure. a. Draw and label the forces acting on the ladder. b. Determine the magnitude of the normal force acting on the ladder at end A and B. c. As the angle of the ladder with the wall reduced, explain what happens to the force acting on the ladder at end A. Answer: (b) 30 N and 50 N ; (c) Decrease, u think 5. A car tyre has a diameter of 560 mm. Determine a. the distance moved by a point on the tyre tread when it rotates through 1 rad b. the angular velocity of the wheel if it completes 10 revolutions per second Answer: (a) 280 mm ; (b) 20π rad s The angular velocity of a car wheel changes from 4 rad s -1 to 20 rad s -1 in 25 s. If the when has a radius of 350 mm, determine a. the average angular acceleration of the wheel b. average tangential linear acceleration of a point on the rim of the wheel Answer: (a) 0.64 rad s -2 ; (b) 0.22 m s An engine requires 5 s to go from its idling speed of 600 r.p.m. to 1200 r.p.m. Determine a. the angular acceleration the engine b. the angular displacement engine c. the number of revolution it makes in this time period Answer: (a) rad s -2 ; (b) rad ; (c) 75.1 rev 8. A phonograph turntable initially rotating at 3.5 rad s -1 makes three complete rotations before coming to stop. Determine a. the angular acceleration of the turntable b. the time taken to come to stop Answer: (a) rad s -1 ; (b) 10.8 s 10 P a g e

5 11 9. A 200 g coin is placed 10 cm from the center of the spinning disc. The mass of the spinning disc is 500 g and it has a radius of 20 cm. Determine a. the moment of inertia of the disc b. the moment of inertia of the coin c. the total moment of inertia of the system Given I disc = MR 2 and I hollow = MR 2 Answer: (a) 0.01 kg m 2 ; (b) kg m 2 ; (c) kg m A torque of 15 N m is applied to s flywheel initially at rest, which then completes 5 revolution in 2.0 s. Calculate a. its angular acceleration b. its moment of inertia Answer: (a) 2.5 rad s -2 ; (b) 1.9 kg m A flywheel of moment of inertia I is rotating from rest to an angular velocity of 20 rad s -1 in 5 s by applying a uniform tangential force of 100 N. If the radius of the flywheel is 50 cm, calculate a. the angular acceleration b. the torque on the flywheel c. the moment of inertia of the flywheel Answer: (a) 4 rad s -2 ; (b) 50 N m ; (c) 12.5 kg m A uniform disk with mass 2.5 kg and radius 20 cm, mounted on a fixed horizontal axle. A block with mass 1.2 kg hangs from a massless cord that is wrapped around the rim of the disk. Calculate a. the acceleration of the falling block b. the tension in the cord Given I disk = MR 2 Answer: (a) 4.8 m s -2 ; (b) 6 N 13. A cylinder of mass 12 kg and radius 0.20 m is rolling along a plane with a translational velocity of 0.30 m s -1. The moment of inertia of the cylinder is 0.24 kg m 2. Determine the total kinetic energy of the cylinder. Answer: 0.81 J 11 P a g e

6 A 5 kg solid cylindrical roller is released from rest down an inclined plane. The inclined plane has a height of 10 m and with an angle of inclination θ = sin -1 ( ). The radius of the roller is 20 cm and its moment if inertia is I = MR 2. Determine the angular velocity of the roller when it reaches the bottom of the slope. Answer: rad s A horizontal merry-go-round has a radius of 2.40 m and a moment of inertia 2100 kg m 2 about a vertical axle through its centre. A tangential force of magnitude 18.0 N is applied to the edge of the merry-go-round for 15.0 s. If the merry-go-round is initially at rest and ignore the frictional torque, determine a. the angular acceleration of the merry-go-round b. the rotational kinetic energy of the merry-go-round after 15.0 s c. the total work done by the force on the merry-go-round d. the average power supplied by the force (Given g = 9.81 m s 2 ) Answer: (a) rad s -2 ; (b) 100 J ; (c) 100 J ; (d) 6.67 W 16. A turntable is rotating freely about an axis with an angular velocity of 6.0 rad s -1 and has a moment of inertia of 1.5 kg m 2. A rough disc is gently dropped on the turn table so that the center coincide. Eventually the combined turntable and dics rotate at 4.5 rad s -1. Determine the moment of inertia of the combined turntable and dics about the rotation axis. Answer: 2 kg m A turntable of moment of inertia 20 kg m 2 is rotating at an angular velocity 10 rad s -1. A disc of moment of inertia 5 kg m 2 is then placed on top of the turntable. Determine the resultant angular velocity of the turntable and the disc. Answer: 8 rad s An ice skater is rotating, with her arm folded at an angular speed of 8.0 rad s -1 when her moment of inertia is 1.8 kg m 2. To slow down she stretches out her hands so that her moment of inertia increases to 4.5 kg m 2. Calculate a) The new angular velocity b) The change in her angular kinetic energy Answer: (a) 3.2 rad s -1 ; (b) J 12 P a g e

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