8.01x - Lect 24 - Rolling Motion, Gyroscopes, VERY NON-INTUITIVE

Lectures by Walter Lewin. They will make you ♥ Physics.・2 minutes read

Torque, angular momentum, and friction play significant roles in understanding rolling objects on slopes, with pure roll occurring when objects roll without skidding. The concept is further demonstrated through the behavior of spinning wheels, showing how torque and angular momentum interact to create unexpected movements and stabilize objects like bicycle wheels and inertial guidance systems.

Insights

  • Friction plays a significant role in preventing skidding or slipping of rolling objects on slopes, emphasizing its crucial function in maintaining stability and control.
  • The interaction between torque and angular momentum leads to unexpected movements in spinning wheels, showcasing the complexities of rotational dynamics and highlighting the nonintuitive behavior exhibited by gyroscopes and inertial guidance systems.

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Recent questions

  • What is pure roll?

    Rolling without skidding or slipping.

  • How does friction affect rolling objects?

    Prevents skidding or slipping.

  • What is the outcome of a race between solid cylinders?

    Neither wins.

  • What happens when torque is applied to a spinning wheel?

    Unexpected rotations occur.

  • How does spin angular momentum impact stability?

    Prevents falling in objects.

Related videos

Summary

00:00

Rolling Objects on Slopes: Torque and Momentum

  • Torque and angular momentum are crucial in understanding rolling objects on slopes.
  • Pure roll occurs when an object rolls without skidding or slipping.
  • In pure roll, the velocity of the center point and the circumference are equal.
  • Friction is essential in preventing skidding or slipping of rolling objects.
  • The acceleration of a cylinder rolling down a slope can be calculated using specific equations.
  • In a race between solid cylinders of different radii but the same mass and length, neither wins.
  • The mass, radius, and length of solid cylinders do not affect their race outcomes.
  • A hollow cylinder will always lose in a race against a solid cylinder, regardless of mass or length.
  • Gyroscopes exhibit nonintuitive behavior due to changes in angular momentum.
  • Torquing a spinning wheel in different directions results in unexpected rotations, showcasing the complexities of angular momentum.

16:36

"Torque and Precession: Wheel's Angular Momentum"

  • The spin angular momentum of a rotating wheel cannot continue indefinitely due to the absence of torque once released.
  • To demonstrate this concept, a wheel is spun towards an observer, with torque applied for a brief period, adding angular momentum in a specific direction.
  • After the torque is stopped, nature resolves the issue by tilting the wheel and making it spin in a different direction, ultimately coming to a standstill.
  • Torque applied to a spinning wheel causes unexpected movements, with the spin angular momentum following the direction of the external torque.
  • The concept is reiterated with the spin angular momentum aligning with the torque direction, leading to the wheel's movement.
  • Precession, the motion resulting from torque on a spinning wheel, is showcased through various demonstrations.
  • The precession frequency is derived based on the torque and spin angular momentum, with the period of precession calculated accordingly.
  • Factors affecting precession frequency include the strength of torque and spin angular momentum, influencing the wheel's movement.
  • The total angular momentum of a spinning and precessing wheel is the sum of the two, with restrictions on the dominance of spin angular momentum.
  • The precession ceases when the wheel stops spinning, emphasizing the interplay between torque, spin angular momentum, and precession.

33:04

"Spinning Wheel Stability in Inertial Guidance"

  • The bicycle wheel has a length of 17 centimeters and a radius of about 29 centimeters, with an assumption that all mass is at the circumference.
  • The moment of inertia is calculated as MR squared, with omega being 2pi times the spin frequency.
  • The angular frequency of precession is determined as rg divided by omega s times R squared, resulting in a precession period of about ten seconds.
  • By increasing torque with added weight, the precession frequency increases, demonstrating the impact of torque on the spinning wheel.
  • The stabilizing effect of spin angular momentum is highlighted, preventing falling in objects like a bicycle wheel, a quarter, and a top.
  • Inertial guidance systems utilize spinning wheels mounted to prevent torque on the axis of rotation, aiding in maintaining direction in vehicles like planes or missiles.
  • The concept of spin angular momentum's stability is crucial in inertial guidance systems, where the spinning wheel's direction remains constant despite external forces.
  • By adding weight to the spinning wheel's axis, the spin angular momentum chases the torque, showcasing the nonintuitive behavior of the system.
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