Assignment 3.3: Uniform Circular Motion

(CONCEPTUAL QUESTIONS)

  1. Describe uniform circular motion?
  1. How is there is an acceleration even though the object is going at a constant velocity in uniform circular motion?
  1. What does uniform mean when discussing uniform circular motion?
  1. What is the distance that it takes to make the complete circle called?
  1. What is the time it takes for an object to make a complete rotation called?
  1. In what direction is the velocity vector pointed in uniform circular motion?
  1. In what direction is the acceleration vector always pointed?
  1. What does centripetal mean?

(PROBLEMS)

  1. A runner moving at a speed of a 8.8 m/s rounds a bend with a radius of 25 m. What is the centripetal acceleration of the runner?
  1. A car racing on a flat track travels at 22 m/s around a curve with a 56 m radius. Find the car’s centripetal acceleration.
  1. An airplane traveling a 201 m/s makes a turn. What is the smallest radius of the circular path (in km) that the pilot can make and keep the centripetal acceleration under ?
  1. A woman rides a carnival Ferris wheel at radius 15 m, completing five turns about its horizontal axis every minute. What are

(a)the period of the motion?

(b)the magnitude of her centripetal acceleration at the highest point?

(c)the direction of her centripetal acceleration at the highest point?

(d)the magnitude of her centripetal acceleration at the lowest point?

(e)The direction of her centripetal acceleration at the lowest point?

  1. When a large star becomes a supernova, its core may be compressed so tightly that it becomes a neutron star, with a radius of about 20 km. If a neutron star rotates once every second,

(a)What is the speed of a particle on the star’s equator?

(b)What is the magnitude of the particle’s centripetal acceleration?

(c)If the neutron star rotates faster, do the answer to (a) and (b) increase, decrease, or remain the same?

  1. An Earth satellite moves in a circular orbit 640 km above Earth’s surface with a period of 98.0 min. What are the (a) speed and (b) magnitude of the centripetal acceleration of the satellite? (Earth’s Radius is )
  1. (Difficult) A boy whirls a stone in a horizontal circle of radius 1.5 m and at height 2.0 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 10 m. What is the magnitude of the centripetal acceleration of the stone during the circular motion?
  1. You go to the county fair and decide to ride the ride called The Graviton. It is the ride that stimulates a stronger gravitational force by spinning in uniform circular motion. If the Graviton rotates at a constant velocity of 16.0 m/s, and has a radius of approximately 5.50 meters, then what is

(a)The uniform circular acceleration of a person on the ride?

(b)The period of revolution of a person on the ride?

  1. A space station is the shape of a ring with a diameter of 450 meters. It is being spun so that an astronaut’s centripetal acceleration is equal to that of gravity on Earth’s surface. How many rotations per minute must it spin for the centripetal acceleration to be equal to the acceleration of gravity on Earth?

(ANSWERS)

  1. 8.1 km

(a)12 s

(b)

(c)Down

(d)

(e)

(a)

(b)

(c)

(a)6. 53 km/min, 392 km/h, 109 m/s

(b)

(a)

(b)

Therefore, it must make two rotations a minute to simulate the acceleration of Earth’s gravity.