Topic 6 Circular Motion and Gravitation Exam-Style Questions 1 a) Calculate the angular velocity of a person standing on the Earth s surface at sea level. b) The summit of Mount Everest is 8848m above sea level. Calculate the difference in linear (tangential) velocity between a person standing on the summit of Mount Everest and at sea level. 1 www.aceyourphysicsexams.com
2 Two markers, red and blue, are attached to a bike wheel as shown. The bike wheel rotates uniformly about its horizontal axis. The magnitude of the angular velocity of the red marker is ω red and the magnitude of the linear (tangential) velocity of the red marker is v red. Which of the following rows correctly compares the relative angular and linear velocity of the blue marker? A B C D Magnitude of Blue Angular Velocity, ω blu e Equal to ω red Greater than ω red Equal to ω red Less than ω red Magnitude of Blue Linear Velocity, v blu e Greater than v red Greater than v red Equal to v red Less than v red 2 www.aceyourphysicsexams.com
3 a) The moon rotates the Earth and completes one complete rotation is 28 days. The moon has a radius of 3.85x10 8 m from the centre of the Earth and has a mass of 7.35x10 22 kg. Calculate the tangential velocity of the moon. b) Calculate the centripetal force acting on the moon as it orbits the Earth. c) Calculate the mass of the Earth. 3 www.aceyourphysicsexams.com
4 Two satellites, x 1 and x 2, of equal mass orbit the Earth as shown. The ratio of centripetal force felt by x 1 to that felt by x 2 is calculated as: A. B. C. D. 1 4 4 1 2 8 4 www.aceyourphysicsexams.com
5 A bucket of water of mass 1.5kg is swung in a vertical loop without any water falling out. The tangential velocity of the bucket at the bottom and top of the loop is 11.2ms 1 and 6.8ms 1 respectively. a) Name the force producing circular motion in this situation. b) Calculate the centripetal force of the bucket at the top and bottom of the loop. c) Calculate the tension in the wire at the top and bottom of the loop. 5 www.aceyourphysicsexams.com
6 A planet is in orbit around a star with radius, r(m). It has a centripetal acceleration, a(ms 2 ). Which of the following is a correct expression for the period, T(s), of the planet in its orbit about the star? A. T 2 = 4π2 r 2 a B. C. T = 2πr 1 2 ar T 2 = 4π2 r a D. T = 2πr 1 2 a 2 r 7 a) State Newton s Universal Law of Gravitation. 6 www.aceyourphysicsexams.com
b) A moon of mass, m, orbits planet X of mass, M. Derive the following relationship between the period of the moon, T and the radius of orbit, R. T 2 = 4π2 R 3 GM 7 www.aceyourphysicsexams.com
c) The moon at point P above planet X gives rise to a gravitational field strength of g at point P as shown below: As planet X orbits within its solar system, it aligns with Planet Y as shown below. Planet Y has the same mass as Planet X and is twice the distance from Point P. Calculate the resultant gravitational field strength felt at P in terms of g. 8 www.aceyourphysicsexams.com
8 A tennis ball of mass m = 0.5kg is tethered to a post and is made to rotate around the post in a horizontal circle of radius r = 0.33m at a constant speed, as shown below: a) On the diagram above, draw and label arrows to represent the forces acting on the tennis ball in the position shown. b) Calculate the resultant force acting on the ball. 9 www.aceyourphysicsexams.com
8 c) CONTINUED Determine the constant speed of rotation of the ball. 9 Which single condition enables Newton s universal law of gravitation to be used to predict the force between the Earth and the Sun? A. The Earth and the Sun both have a very large radius. B. The distance between the Earth and the Sun is approximately constant. C. The Earth and the Sun both have a very large mass. D. The Earth and the Sun behave as point masses. 10 www.aceyourphysicsexams.com