Torque,stability and equilibrium
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1. Torque is a vector quantity that determines the ability of a force to introduce rotation. It is calculated as the product of the force and the lever arm (perpendicular distance from the axis of rotation to the line of force). 2. Torque depends on three factors: the magnitude of the applied force, the distance from the point of application to the pivot, and the angle of the applied force. 3. The lever arm used in torque calculations must be the perpendicular distance from the axis of rotation to the line of action of the force.
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This document discusses kinetics of particles and Newton's laws of motion. It introduces the concept of equation of motion relating the forces acting on a particle to its acceleration. Equations of motion are developed for rectangular, normal-tangential, and cylindrical coordinate systems. Examples are provided to demonstrate solving equations of motion for particles undergoing accelerated motion under various force conditions in different coordinate systems.
Chapter 1 - Rotational Dynamics.pptx
MAHARASHTRA STATE BOARD
PHYSICS
CHAPTER 1
ROTATIONAL DYNAMICS
CONTENT
Moment of Inertia
Torque
Angular Momentum
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This document discusses different types of torsion meters used to measure torque. It defines torque as a twisting force that tends to cause rotation, with the unit being Newton meters. Torque can be computed by measuring the force F at a known radius r, using the formula T = Fr. Common torsion meters mentioned include:
1. Mechanical torsion meters, which measure torque by varying a known mass or distance to equal the torque value to be measured.
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- Formulas relate angular quantities like speed (ω) and displacement (θ) to linear quantities like speed (v) and arc length (s) using the radius (R).
- Centripetal force (Fc) is required to cause circular motion and is given by Fc = Mv2/R, where M is the object's mass and v is its speed.
- Banked roads allow vehicles to safely take curved portions faster by providing tilt that replaces needed friction with
line and surface integral.pptx .
The document discusses various types of integrals in vector calculus:
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- Flux integrals involve the velocity of a fluid across a closed surface or curve, with applications to circulation and solenoidal functions.
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Torque,stability and equilibrium
- 1. *door top view F1 F2 axis of rotation r1 r2 Where: F = force r = lever arm= perpendicular distance from the axis of rotation to the line along which the forces acts. here., α∝ F
- 2. *door top view F1 F2 axis of rotation r1 r2 α ∝ F x r Moment of Force or Torque (τ) α ∝ τ
- 3. a vector quantity that determines the ability of a force to introduce rotation. τ = rF ; unit: mN 1.Magnitude of the applied force 2.Distance from point of application to pivot (location of applied force) 3.Angle ( direction of the applied force)
- 4. F1 F2 F3 r1 r2 τ F1 > τ F2 τ F2 < τ F1 τ = 0 NOTE: in general τ = r⊥F Remind us that we must use the distance from the axis of rotation that is perpendicular to the line of action of the force r⊥ = r sin ⴱ
- 5. F2 ⴱ τ = rF⊥ l = rF⊥ sinⴱ We can use τ = r⊥ F or τ = r F⊥ or τ = r F sin ⴱ to calculate the torque whichever is easiest. Line of action of a force - the line of motion of a force is an imaginary line of indefinite length drawn a long the direction of the force The moment arm is the perpendicular distance from the line of action of a force to the axis of rotation.
- 6. 1. An 80 N acts at the end of a 12 cm wrench as shown. Find the torque. 80 N 12 cm ⴱ =60o 2. Find the resultant torque about axis A for the arrangement shown: ⴱ =30o ⴱ =30o 4 m 2 m6 m F3 =20 N F2 = 40N F1 =30 N
- 7. Torque is a vector quantity that has a direction as well as magnitude Thumb F (force) Pointer r (moment arm) Middle finger direction of τ (torque)
- 9. ↑ Up + ↓ Down - → Right + ← left - ⊙ Outward + ⊗ Inward - CC Counterclockwise + C clockwise -
- 10. → ⊗ ↑ ← ⊙ ⊙ → ↑ ↑
- 11. Car at rest Constant speed, no change in direction An object is said to be in equilibrium if it does not have linear acceleration and angular acceleration Linear acceleration is Zero if….
- 12. Angular acceleration is Zero if…. wheel at rest Constant rotation
- 15. The center of mass lies at the geometric center for a symmetric, uniform density object. h/3 h R h/2 h h/2 h
- 16. The center of mass can be outside the mass of the body. Center of mass
- 17. Ability of an object to return to its original position after it is displaced or tilted slightly - CG is below of point of support - the objects return to its original position - When object is displaced, the object moves even farther from its position - When object is displaced, the object remain in its position
- 21. cm