Circular Motion Notes PDF

Chapter 1 SP 014 Exercise 1 1. A particle is moving on a circular path of radius 0.5 m at a constant speed of 10 ms -1. Find the time taken to completer 20 revolutions. [t = 6.28 s...

Chapter 1 SP 014 Exercise 1 1. A particle is moving on a circular path of radius 0.5 m at a constant speed of 10 ms -1. Find the time taken to completer 20 revolutions. [t = 6.28 s] 2. What are the angular velocities of the hour-hand and minute-hand of a clock? [1.45 x 10-4 rad s-1; 1.75 x 10-3 rad s-1] 3. The speed of an object in uniform circular motion is 6.0 ms-1, the diameter of the circle is 2.5 m. What is it angular velocity? [4.8 rad s-1] 4. A particle moving in a circle takes 0.25 s to completer one revolution. How many complete revolutions per minute (rpm) does the particle perform? [240 rpm] 5. A particle in uniform circular motion takes 3.0 s to move from one end A of a diameter to the other end B. the diameter of the circle is 5.00 cm. Calculate: (a) the angular velocity, (b) the speed. [1.05 rads-1; 2.62 x 10-2 ms-1] 6. An object is moving in a circle of radius 40 cm with constant angular velocity of 6 rads-1. Find: (a) the velocity of the object, (b) the time for one complete revolution. [2.4 ms-1; 1.05 s] 7. A 200 g of mass is moving with uniform angular velocity in a circle of radius 80 cm on a smooth horizontal surface. If the mass completed 10 revolutions in one second, calculate: (a) the angular velocity, (b) the linear velocity. [62.8 rads-1; 50.3 ms-1] 8. If a disc 30 cm in diameter rolls 65 m along a straight line without slipping, calculate: (a) the number of revolutions would it makes in the process, (b) the angular displacement would be through by a speck of gum on its rim. [69 rev; 138 rad] 9. During a certain period of time, the angular displacement of a swinging door is described by 𝜃 = 5.00 + 10.0𝑡 + 2.00𝑡 2 where  is radians and t is in seconds. Determine the angular displacement, angular speed and angular acceleration, (a) at time t = 0 s, (b) at time t = 3.00 s. [5.00 rad; 10.0 rads-1; 4.00 rads-2; 53.0 rad; 22.0 rads-1; 4.00 rads-2] 10. A disk 8.00 cm in radius rotates at a constant rate of 1200 rev min-1 about its central axis. Determine: (a) its angular speed, (b) the tangential speed at a point 3.00 cm from its centre, (c) the radial (centripetal) acceleration of a point on the rim, (d) the total distance a point on the rim moves in 2.00 s. 11. A 0.35 m diameter grinding wheel rotates at 2500 rpm. Calculate: (a) its angular velocity in rad s-1, 53 Chapter 1 SP 014 (b) the linear speed and the radial / centripetal acceleration of a point the edge of the grinding wheel. 12. A rotating wheel required 3.00 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.00 s interval is 98.0 rad s-1. Calculate the constant angular acceleration of the wheel. 13. A wheel rotates with a constant angular acceleration of 3.50 rad s-2. (a) if the angular speed of the wheel is 2.00 rad s-1 at t = 0, through what angular displacement does the wheel rotate in 2.00 s? (b) through how many revolutions has the wheel turned during this time interval? (c) what is the angular speed of the wheel at t = 2.00 s? 14. A bicycle wheel is being tested at a repair shop. The angular velocity of the wheel is 4.00 rad s-1 at time t = 0, and its angular acceleration is constant and equal -1.20 rad s-2. A spoke OP on the wheel coincides with the +x-axis at time t = 0 as show in figure below. (a) What is the wheel’s angular velocity at t = 3.00 s? (b) What angle in degree does the spoke OP make with the positive x-axis at this time? 15. The bobsled track at the 1994 Olympics in Norway, contained turns with radii of 33 m and 24 m, as figure below illustrates. Find the centripetal acceleration at each turn for a speed of 34 m s-1. 16. Imagine that you are a passenger in a car, not wearing a seat belt. The car makes a sharp right turn. What will happen to you? 54 Chapter 1 SP 014 17. Find the centripetal acceleration of a sample which is at a distance of 5.0 cm from the axis of rotation of a centrifuge rotating at a constant speed of 2000 revolutions per minute. 18. A ball of mass 0.35 kg is attached to the end of a horizontal cord and is rotated in a circle of radius 1.0 m on a frictionless horizontal surface. If the cord breaks when the tension in it exceeds 80 N, determine: (a) the maximum speed of the ball, (b) the minimum period of the ball. 19. A 0.075 kg toy airplane is tied to the ceiling with a string. When the airplane’s motor is started it moves with a constant speed of 1.21 m s-1 in a horizontal circle of radius 0.44 m. Find: (a) the angle the string makes with the vertical. (b) the tension in the string. 20. A woman of mass 60 kg stands at the rim of a horizontal turntable having a moment of inertia of 500 kg m2 and a radius of 2.00 m. the turntable is initially at rest and is free to rotate about the frictionless vertical axle through its centre. The woman then starts walking around the rim clock wise (as viewed from above the system) at a constant speed of 1.50 m s-1 relative to the Earth. (a) In what direction and with what value of angular speed does the turntable and with what value of angular speed does the turntable rotate? (b) How much work does the woman do to set herself and the turntable into motion? 21. Determine the angular momentum of the Earth. (a) about its rotation axis (assume the Earth is a uniform solid sphere), and (b) about its orbit around the Sun (treat the Earth as a particle orbiting the Sun). [Given MEarth = 6.0 x 1024 kg, R = 6.4 x 106 m, r = 1.5 x 108 km] 22. Calculate the magnitude of the angular momentum of the second hand on a clock about an axis through the centre of the clock face. The clock hand has a length of 15.0 cm and a mass of 6.00 kg. Take the second hand to be a thin rod rotating with angular velocity about one end. (Given the moment of inertia of thin rod about the axis through the CM is 1 𝑀𝐿2 ) 12 END 55