Ch 12: Torque & Rotational DynamicsWorksheetSee 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: Intro to Torque

Example #1: Torque of fish pulling on pole

Practice: A 4 m-long ladder rests horizontally on a flat surface. You try to lift it up by pulling on the left end of the ladder with a force of 50 N that makes an angle of 37° with the vertical axis. Calculate the torque that your force produces, about an axis through the other (right) end of the ladder.

Example #2: Maximum torque on wrench

Practice: You pull with a 100 N at the edge of a 25 cm long wrench, to tighten a bolt (gold), as shown. The angle shown is 53° . Calculate the torque your force produces on the wrench, about an axis perpendicular to it and through the bolt.

Additional Problems
In cars, a gear train (shown in the figure) is used in the transmission to allow the wheels of the car to rotate at high angular speeds while at low engine rpm's, allowing for less gas to be used. If the drive gear in a gear train is connected directly the engine, and the driven gear directly to the wheels (meaning both rotate with their respective gears), how much torque would be delivered to the wheels when the torque produced by the engine is 100 Nm and the drive gear is 3 times larger than the driven gear?
A gasoline engine produces power and torque as shown in the following figure. In a direct drive configuration, the wheels of a car spin with the same angular speed as the engine does. If the wheels have a diameter of 45 cm, how fast would the car have to be moving in order for the engine to be producing maximum power? What about maximum torque? 
Two equal forces are applied to a door. The first force is applied at the midpoint of the door, the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque? A) both exert equal non-zero torques B) the first at the midpoint C) both exerts zero torques D) the second at the doorknob E) additional information is needed
A wrench is acting on a nut. The nut is at the origin and the wrench extends from the nut along the +x-axis. A force of 150 N acts on the wrench at the position x = 15.0 cm at an angle of 30.0°. What is the torque the wrench exerts on the nut? A) 1949 N•m B) 11.3 N•m C) 19.5 N•m D) 2250 N•m E) 22.5 N•m
In the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface. The crate weighs 930 N, and its center of gravity is at its geometric center. A horizontal force F is applied at a distance h above the floor. If h = 0.61 m, what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide. A) 763 N B) 688 N C) 305 N D) 413 N
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. For an axis at the hinge, what is the torque due to the weight of the bar?
A wheel is rotating clockwise on a fixed axis perpendicular to the page (x). A torque that causes the wheel to slow down is best represented by the vector A. 1 B. 2 C. 3 D. 4 E. 5