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Torque and rotation exercises · Physics Playground

ExercisesPhysics

Torque and rotation

27 problems with worked solutions, from College Physics.

Start with a random one

Learn it first: Torque & Balance, Spinning & Angular Momentum

College Physics9.2 The Second Condition for Equilibrium

Example 9.1She Saw Torques On A SeesawThe two children shown in Figure 9.8 are balanced on a seesaw of negligible mass. (This assumption is made to keep the example simple—more involved examples will follow.) The first child has a mass of 26.0 kg and…

College Physics9.4 Applications of Statics, Including Problem-Solving Strategies

Example 9.2What Force Is Needed to Support a Weight Held Near Its CG?For the situation shown in Figure 9.19, calculate: (a) FR, the force exerted by the right hand, and (b) FL, the force exerted by the left hand. The hands are 0.900 m apart, and the cg of the pole is 0.600 m from the…

College Physics9.5 Simple Machines

Example 9.3What is the Advantage for the Wheelbarrow?In the wheelbarrow of Figure 9.23, the load has a perpendicular lever arm of 7.50 cm, while the hands have a perpendicular lever arm of 1.02 m. (a) What upward force must you exert to support the wheelbarrow and its…

College Physics9.6 Forces and Torques in Muscles and Joints

Example 9.4Muscles Exert Bigger Forces Than You Might ThinkCalculate the force the biceps muscle must exert to hold the forearm and its load as shown in Figure 9.26, and compare this force with the weight of the forearm plus its load. You may take the data in the figure to…
Example 9.5Do Not Lift with Your BackConsider the person lifting a heavy box with his back, shown in Figure 9.29. (a) Calculate the magnitude of the force FB– in the back muscles that is needed to support the upper body plus the box and compare this…

College Physics10.1 Angular Acceleration

Example 10.1Calculating the Angular Acceleration and Deceleration of a Bike WheelSuppose a teenager puts her bicycle on its back and starts the rear wheel spinning from rest to a final angular velocity of 250 rpm in 5.00 s. (a) Calculate the angular acceleration in rad/s^2. (b) If she now slams…
Example 10.2Calculating the Angular Acceleration of a Motorcycle WheelA powerful motorcycle can accelerate from 0 to 30.0 m/s (about 108 km/h) in 4.20 s. What is the angular acceleration of its 0.320-m-radius wheels? (See Figure 10.6.) Figure 10.6 The linear acceleration of a…With a figure
Quick checkAngular acceleration is a vector, having both magnitude and direction. How do we denote its magnitude and direction? Illustrate with an example.

College Physics10.2 Kinematics of Rotational Motion

Example 10.3Calculating the Acceleration of a Fishing ReelA deep-sea fisherman hooks a big fish that swims away from the boat pulling the fishing line from his fishing reel. The whole system is initially at rest and the fishing line unwinds from the reel at a radius of 4.50…
Example 10.4Calculating the Duration When the Fishing Reel Slows Down and StopsNow let us consider what happens if the fisherman applies a brake to the spinning reel, achieving an angular acceleration of –300rad/s^2. How long does it take the reel to come to a stop?
Example 10.5Calculating the Slow Acceleration of Trains and Their WheelsLarge freight trains accelerate very slowly. Suppose one such train accelerates from rest, giving its 0.350-m-radius wheels an angular acceleration of 0.250rad/s^2. After the wheels have made 200 revolutions (assume…
Example 10.6Calculating the Distance Traveled by a Fly on the Edge of a Microwave Oven PlateA person decides to use a microwave oven to reheat some lunch. In the process, a fly accidentally flies into the microwave and lands on the outer edge of the rotating plate and remains there. If the plate has a…
Quick checkRotational kinematics has many useful relationships, often expressed in equation form. Are these relationships laws of physics or are they simply descriptive? (Hint: the same question applies to linear kinematics.)

College Physics10.3 Dynamics of Rotational Motion: Rotational Inertia

Example 10.7Calculating the Effect of Mass Distribution on a Merry-Go-RoundConsider the father pushing a playground merry-go-round in Figure 10.13. He exerts a force of 250 N at the edge of the 50.0-kg merry-go-round, which has a 1.50 m radius. Calculate the angular acceleration produced…With a figure
Quick checkTorque is the analog of force and moment of inertia is the analog of mass. Force and mass are physical quantities that depend on only one factor. For example, mass is related solely to the numbers of atoms of various…

College Physics10.4 Rotational Kinetic Energy: Work and Energy Revisited

Example 10.8Calculating the Work and Energy for Spinning a GrindstoneConsider a person who spins a large grindstone by placing her hand on its edge and exerting a force through part of a revolution as shown in Figure 10.17. In this example, we verify that the work done by the torque…
Example 10.9Calculating Helicopter EnergiesA typical small rescue helicopter, similar to the one in Figure 10.18, has four blades, each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis…
Example 10.10Calculating the Speed of a Cylinder Rolling Down an InclineCalculate the final speed of a solid cylinder that rolls down a 2.00-m-high incline. The cylinder starts from rest, has a mass of 0.750 kg, and has a radius of 4.00 cm.
Quick checkAnalogy of Rotational and Translational Kinetic EnergyIs rotational kinetic energy completely analogous to translational kinetic energy? What, if any, are their differences? Give an example of each type of kinetic…

College Physics10.5 Angular Momentum and Its Conservation

Example 10.11Calculating Angular Momentum of the Earth
Example 10.12Calculating the Torque Putting Angular Momentum Into a Lazy SusanFigure 10.21 shows a Lazy Susan food tray being rotated by a person in quest of sustenance. Suppose the person exerts a 2.50 N force perpendicular to the lazy Susan’s 0.260-m radius for 0.150 s. (a) What is the final…With a figure
Example 10.13Calculating the Torque in a KickThe person whose leg is shown in Figure 10.22 kicks his leg by exerting a 2000-N force with his upper leg muscle. The effective perpendicular lever arm is 2.20 cm. Given the moment of inertia of the lower leg is 1.25…With a figure
Example 10.14Calculating the Angular Momentum of a Spinning SkaterSuppose an ice skater, such as the one in Figure 10.23, is spinning at 0.800 rev/ s with her arms extended. She has a moment of inertia of 2.34kg⋅m^2 with her arms extended and of 0.363kg⋅m^2with her arms close to…
Quick checkIs angular momentum completely analogous to linear momentum? What, if any, are their differences?

College Physics10.6 Collisions of Extended Bodies in Two Dimensions

Example 10.15Rotation in a CollisionSuppose the disk in Figure 10.26 has a mass of 50.0 g and an initial velocity of 30.0 m/s when it strikes the stick that is 1.20 m long and 2.00 kg. (a) What is the angular velocity of the two after the collision?…
Quick checkIs rotational kinetic energy a vector? Justify your answer.

College Physics10.7 Gyroscopic Effects: Vector Aspects of Angular Momentum

Quick checkRotational kinetic energy is associated with angular momentum? Does that mean that rotational kinetic energy is a vector?