🔖 Topics

  • Translational vs. Rotational Motion
  • Review of Radians
  • Translation to Rotation Analogs
  • Centripetal Force and Acceleration
  • Uniform Circular Motion

🎯 Objectives

  • Qualitatively discuss angular motion / velocity / acceleration concepts
  • Calculate centripetal force and acceleration for a rotating rigid body
  • Calculate the properties of a body in uniform circular motion

📋 Sequence

  • Introduce Rotational Motion
  • Rotation / Uniform Circular Motion Examples

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

Rolling Wheel: A wheel with a diameter of 0.75 meters is rolling without slipping along the floor. It is moving with a translational velocity of 5.0 m/s.

  • Draw a free-body diagram of the rolling wheel.
  • How long does it take for the wheel to make one complete turn?
  • Would it take more or less time for the wheel to make one complete turn if I increase the diameter of the wheel?
  • Would it take more or less time for the wheel to make one complete turn if I increase the translational velocity of the wheel?
  • Would static or kinetic friction come into play while the wheel rolls without slipping?
  • Bonus: Use your answer to the previous question to explain why anti-lock breaking systems allow your car wheels to turn sporadically while breaking. Hint: generally, the coefficient of static friction is larger than the coefficient of kinetic friction between two surfaces.

Puck on a Table: A puck with a mass of 0.5 kg is tied to a string of length 20 cm, which is in turn tied to a pin on a frictionless table. The puck is pushed so that it undergoes uniform circular motion with an angular speed of 20 rad/sec.

  • Draw a free-body diagram of the puck on the table.
  • Which of the forces acting on the puck provide the centripetal force?
  • What is the centripetal force acting on the puck?
  • What is the centripetal acceleration acting on the puck?
  • How would the tension in the string change if I increased the speed of the puck?
  • How would the tension in the string change if I increased the mass of the puck?

Car on a Circular Road: An 850 kg car moving at 20 m/s traverses a circular road with a radius of 70.0 m without slipping.

  • Draw a free-body diagram of the car.
  • Which of the forces acting on the car provide the centripetal force?
  • What is the net force acting on the car?
  • What is the net acceleration acting on the car?
  • Which direction is the force / acceleration pointing?
  • What is the minimum coefficient of friction between the road and the car?

Car on a Banked Circular Road: An 850 kg car traverses a circular road with a radius of 70.0 m. The road is wet with rain (no friction), but it is banked at an angle of \(15^\circ\).

  • Draw a free-body diagram of the car.
  • Which of the forces acting on the car provide the centripetal force?
  • What is the net force acting on the car?
  • What is the net acceleration acting on the car?
  • Which direction is the force / acceleration pointing?
  • At what speed can the car safely traverse the curve without slipping / drifting?
  • What would happen if the car increases its speed while traversing the curve?
  • What would happen if the car decreases its speed while traversing the curve?

Orbiting Bodies: A satellite of mass \(m\) orbits a planet of mass \(M\) at a distance of \(R\) from the center of the planet.

  • Draw a free-body diagram of the satellite in orbit
  • Which of the forces acting on the satellite provide the centripetal force?
  • What is the centripetal force acting on the satellite?
  • What is the centripetal acceleration acting on the satellite?
  • At what speed does the satellite orbit the planet?
  • What would happen if the satellite were to increase its speed?
  • What would happen if the satellite were to decrease its speed?
  • The ISS orbits Earth at a altitude of 420 km above the surface. What is the average speed of the ISS according to Newton’s Laws / centripetal acceleration?

Some helpful information:

  • Mass of Earth: \(5.97219 \times 10^{24} \: kg\)
  • Radius of Earth: \(6378.1 \: km\)
  • Gravitational Constant (G): \(6.6743 \times 10^{-11} \: N \cdot m^2/kg^2\)

✅ Partial Solutions

N/A

📘 Connected Resources

  • Alicia. “The 20 Most Frequently Asked Questions about the International Space Station.” Kennedy Space Center Blog, https://www.kennedyspacecenter.com/blog/the-20-most-frequently-asked-questions-about-the-international-space-station, October 2020.
  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.