Ch 13: Rotational EquilibriumSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Beam / Shelf Against a Wall

Practice: A beam 200 kg in mass and 6 m in length is held horizontally against a wall by a hinge on the wall and a light rod underneath it, as shown. The rod makes an angle of 30° with the wall and connects with the beam 1 m from its right edge. Calculate the angle that the Net Force of the hinge makes with the horizontal (use +/– for above/below +x axis).

Example #1: Beam supporting an object

Practice: A beam 200 kg in mass and 4 m in length is held against a vertical wall by a hinge on the wall and a light horizontal cable, as shown. The beam makes 53° with the wall. At the end of the beam, a second light cable holds a 100 kg object. Calculate the angle that the Net Force of the hinge makes with the horizontal (use +/– for above/below +x axis).

Additional Problems
A solid bar of length L has a mass m 1. The bar is fastened by a pivot at one end to a wall which is at an angle θ with respect to the horizontal. The bar is held horizontally by a vertical cord that is fastened to the bar at a distance x from the wall. A mass m2 is suspended from the free end of the bar. Find the tension in the cord. 1. T = (m1 + 1/2 m2) (L/x) gcosθ 2. T = (m1 + m2) gsinθ 3. T = (m1 + m2) gcosθ 4. T = (m1 + m2) (L/x) (g/2) 5. T = 0 6. T = (m1 + 1/2 m2) (L/x) g 7. T = (m1 + 1/2 m2) (L/x) gsinθ 8. T = (1/2 m1 + m2) (L/x) gsinθ 9. T = (1/2 m1 + m2) (L/x) g 10. T = (1/2 m1 + m2) (L/x) gcosθ
A uniform metal rod, with a mass of 5.0 kg and a length of 2.0 m, is attached to a wall by a hinge at its base. A horizontal wire is bolted to the wall above the base of the rod and holds the rod at an angle of 30° above the horizontal. The wire is attached to the top of the rod. (a) Find the tension in the wire. (b) Find the horizontal and vertical components of the force exerted on the rod by the hinge. Use g = 10 m/s2.
A uniform sign is supported at P as shown in the figure. If the sign is a square 0.7 m on its mass is 7.0 kg. What is the magnitude of the horizontal force that P experiences? A) 24 N B) 98 N C) 34 N D) 0 N
A uniform bar with mass 50 kg and length 4.0 m is attached to a wall by a frictionless hinge. The bar is held in a horizontal position by a light rope that is attached at the end of the bar. The other end of the rope is attached to the wall. The rope makes an angle of 30° with the wall. What is the magnitude of the resultant force that the hinge exerts on the bar?
A horizontal, nonuniform beam of mass M and length ℓ is hinged to a vertical wall at one side, and attached to a wire on the other end. The bar is motionless and a wire exerts a force T at an angle of φ with respect to the vertical. If the mass of the beam is 7 kg, the tension in the wire is 35 N, sin φ = 3/5 and cos φ = 4/5, how far is the center of mass of the beam from the hinge? The acceleration due to gravity is 10 m/s2. 1. 0.32 ℓ 2. 0.5 ℓ, of course 3. 0.4 ℓ  4. Not enough information is given. 5. 0.18 ℓ 6. 0.16 ℓ 7. 0.375 ℓ 8. 0.666667 ℓ 9. 0.3 ℓ 10. 0.625 ℓ
A uniform bar (I = 1/3 ML2 for an axis at one end) has mass M = 5.00 kg and length L = 6.00 m. The lower end of the bar is attached to the wall by a frictionless hinge. The bar is held stationary at an angle of 60° above the horizontal by a cable that runs from the upper end of the bar to the wall. The cable makes an angle of 37° with the bar. What is the tension in the cable?
A uniform beam 4.30 m long and weighing 2500 N carries a 3200 N weight 1.50 m from the far end, as shown in the figure below. It is supported horizontally by a hinge at the wall and a metal wire at the far end. How strong does the wire have to be? That is, what is the mximum tension it must be able to support withot breaking?
A uniform beam 4.30 m long and weighing 2500 N carries a 3200 N weight 1.50 m from the far end, as shown in the figure below. It is supported horizontally by a hinge at the wall and a metal wire at the far end. What are the horizontal and vertical components of force exerted on the beam by the hinge?
One end of a uniform bar that has weight w is attached to a wall by a fricitonless hinge. The bar is held in a horizontal position by a cable tha makes an angle of 37° with the bar. The tension in the cable is 80.0 N. What is the weight of the bar?
One end of a uniform bar that is 6.0 m long is attached to a vertical wall by a frictionless hinge. The bar is held at an angle of 60° above the horizontal by a horizontal rope that is attached to the other end of the bar, as shown in the sketch. If the tension in the rope is 120 N, what is the mass m of the bar?
A uniform bar has mass 30 kg and length 6.0 m. One of the bar is attached to a vertical wall by a frictionless hinge. A light horizontal cable connects the other end of the bar of the wall and holds the cable at an angle of 37° above the horizontal. What is the tension in the cable?
A uniform bar has mass 30 kg and length 6.0 m. One of the bar is attached to a vertical wall by a frictionless hinge. A light horizontal cable connects the other end of the bar of the wall and holds the cable at an angle of 37° above the horizontal. If the cable is cut, what is the magnitude of the angular acceleration of the bar just after the cable is cut?
A uniform bar has mass 3.00 kg and length 6.00 m. The lower end of the bar is attached to the wall by a frictionless hinge. The bar is held stationary at an angle of 53.1° above the horizontal by a horizontal cable that runs from the upper end of the bar to the wall. For an axis at the hinge, what is the magnitude of the torque produced by the weight of the bar?