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Circular Motion |
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(Assume g = 10 m/s2 or 10 N/kg unless otherwise stated) 1. An object of mass 4 kg moves round a circle of radius 6 m with a constant velocity of 12 m/s. Calculate (i) the angular velocity (ii) the force towards the centre. [Answer: (i) (ii)] 2. A model of car moves round a circular track of radius 0.3 m at 2 revolutions per second. What is (a) the angular velocity w, (b) the period T, (c) the velocity v of the car? (d) Find also the angulat velocity of the car if it moves with a uniform speed of 2 m/s in a circle of radius 0.4 m. [Answer: (a) 4 pi rad/s (b) 4 pi (c) 3.8 m/s (d) 5 rad/s] 3. A stone of mass 0.6 kg, attached to a string of length 0.5 m, is whirled in a horizontal circle at a constant velocity. If the maximum tension (force) in the string is 30 N before it breaks, calculate (a) the maximum velocity of the stone, (b) the maximum number of revolutions per second it can make. [Answer: (a) 5 m/s (b) 1.6 ] 4. A model aeroplane X has a mass of 0.5 kg and has a control wire OX of length 10m attached to it when it flies in a horizontal circle with its wings horizontal. The wire OX is then inclined 60 degree to the horizontal and fixed to a point and X takes 2 s to fly once round its circular path. Calculate (a) the tension in the control wire, (b) the upward force on OX due to the air. [Answer: (a) 49.35 N (b) 48.30 N] 5. A light string carrying a small bob of mass 5.0 x 10-2 kg hangs from the roof of a moving vehicle. (a) What can be said about the motion of the vehicle if the string hangs vertically? (b) The vehicle moves in a horizontal straight line from left to right, with a constant acceleration of 2.0 m/s2. (i) Show in sketch the force acting on the bob. (ii) By resolving horizontally and vertically or by scale drawing, determine the angle which the string makes with the vertical. (c) The vehicle moves down an incline making an angle of 30 degree with the horizontal with a constant acceleration of 3.0 m/s2. Determine the angle which the string makes with the vertical. [Answer: (b) (ii) 11.3 degree (iii) 17 degree] 6. A force of 200 N pulls a sledge of mass 50 kg and overcome a constant frictional force of 40 N. What is the acceleration of the sledge? [Answer: 3.2 m/s2] 7. An object of mass 2.00 kg is attached to the hook of a spring-balance and the balance is suspended vertically from the roof of a lift. What is the reading on the spring-balance when the lift is (i) going up with an acceleration of 0.2 m/s2, (ii) going down with an acceleration of 0.1 m/s2, (iii) ascending with uniform velocity of 0.15 m/s. [Answer: (i) 20.4 N (ii) 19.8 N (iii) 20 N] 8. A car of mass 1000 kg is moving up a hill inclined 30 degree to the horizontal. The total frictional force on the car is 1000 N. Calculate the force due to the engine when the car is (a) accelerating at 2 m/s2 (b) moving with a steady velocity of 15 m/s. [Answer: (a) 8000 N (b) 6000 N]
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