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Ch 10: Dynamics of Rotational Motion
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 10: Dynamics of Rotational MotionProblem 9
Chapter 10, Problem 9

The flywheel of an engine has moment of inertia 1.60 kg/m2 about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in 8.00 s, starting from rest?

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First, convert the angular speed from revolutions per minute (rev/min) to radians per second (rad/s). Use the conversion factor: 1 rev = 2π rad and 1 min = 60 s. The formula is: ω = 400 rev/min × (2π rad/rev) / (60 s/min).
Next, calculate the angular acceleration (α) using the formula: α = (ω - ω₀) / t, where ω₀ is the initial angular speed (0 rad/s since it starts from rest), ω is the final angular speed, and t is the time duration (8.00 s).
Now, use the relationship between torque (τ), moment of inertia (I), and angular acceleration (α) given by the formula: τ = I × α. Here, I is the moment of inertia (1.60 kg/m²) and α is the angular acceleration calculated in the previous step.
Substitute the values of I and α into the torque formula to find the constant torque required to achieve the desired angular speed.
Ensure all units are consistent and check the calculations for any errors. The final expression for torque will give you the magnitude needed to bring the flywheel to the specified angular speed in the given time.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Moment of Inertia

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution relative to the axis of rotation. For a flywheel, it quantifies how much torque is needed to achieve a certain angular acceleration.
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Angular Speed

Angular speed refers to how fast an object rotates or revolves relative to another point, typically the center of rotation. It is usually measured in revolutions per minute (rev/min) or radians per second (rad/s), and is crucial for determining the final rotational state of the flywheel.
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Torque

Torque is a measure of the force that can cause an object to rotate about an axis. It is the rotational equivalent of linear force and is calculated as the product of force and the distance from the axis of rotation. In this context, torque is needed to change the angular speed of the flywheel.
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Related Practice
Textbook Question

A cord is wrapped around the rim of a solid uniform wheel 0.250 m in radius and of mass 9.20 kg. A steady horizontal pull of 40.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. Find the magnitude and direction of the force that the axle exerts on the wheel.

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Textbook Question

Three forces are applied to a wheel of radius 0.350 m, as shown in Fig. E10.4. One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0° angle with the radius. What is the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center?

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Textbook Question

A metal bar is in the xyxy-plane with one end of the bar at the origin. A force F→=(7.00N)i+(−3.00N)j\(\overrightarrow{F}\)=\(\left\)(7.00N\(\right\))i+(-3.00N)j is applied to the bar at the point x=3.00 mx=3.00\(\text{ m}\), y=4.00 my=4.00\(\text{ m}\). What are the magnitude and direction of the torque with respect to the origin produced by F→\(\overrightarrow{F}\)?

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Textbook Question

A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0-N force at the end of the handle at 37° with the handle (Fig. E10.7). What is the maximum torque he could exert with this force, and how should the force be oriented?

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Textbook Question

(a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle? Consult Appendix E and the astronomical data in Appendix F

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Textbook Question

A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0-N force at the end of the handle at 37° with the handle (Fig. E10.7). What torque does the machinist exert about the center of the nut?

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