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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 5: Torque & Rotational DynamicsRotational Inertia

Rotational Inertia (College Board AP® Physics 1: Algebra-Based): Exam Questions

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Rotational Inertia

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1
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Two masses are connected by a light, inextensible string over a frictionless pulley.

If the pulley has rotational inertia, describe how this would affect the acceleration of the masses.

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2
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Diagram of a pulley system with two masses. Object 1 mass is \( m_0 \), Object 2 mass is \( 1.5m_0 \). Pulley radii labelled \( r_0 \) and \( 2r_0 \).

Figure 1

Two pulleys with different radii are attached to each other so that they rotate together about a horizontal axle through their common center. There is negligible friction in the axle. Object 1 has mass m subscript 0 and hangs from a light string wrapped around the larger pulley of radius 2 r subscript 0, while Object 2 has mass 1.5 m subscript 0 and hangs from another light string wrapped around the smaller pulley of radius r subscript 0, as shown in Figure 1. At time t space equals space 0, the pulleys are released from rest and the objects begin to accelerate.

Determine an expression for the rotational inertia of the two-pulley system.

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3
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A horizontal beam of length L hinged to a wall at its left end with a string at angle θ, supporting a block at its right end.

Figure 1

The left end of a uniform beam of mass M and length L is attached to a wall by a hinge, as shown in Figure 1. One end of a string with negligible mass is attached to the right end of the beam. The other end of the string is attached to the wall above the hinge. The beam remains horizontal. The rotational inertia of a beam about its center is 1 over 12 M L squared.

Determine an expression for the rotational inertia of the beam-block system about the hinge.

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A sphere attached to a rod on an axle via a rod. The center of mass of the system is located just below the center of the sphere.

Figure 1

A rod with a sphere attached to the end is connected to a horizontal mounted axle. The mass of the rod is m subscript r and the mass of the sphere is m subscript s space equals space 5 m subscript r. The center of mass of the rod-sphere system is indicated with a circled times, as shown in Figure 1.

A rod-sphere system hanging vertically downward with respect to the axle. Two lengths are indicated, length "L" represents the distance from axle to the bottom of the sphere, and length "3/4 L" represents the distance from the axle to the center of mass.

Figure 2

The rod-sphere system has mass M and length L, the sphere has radius R space equals space 1 over 6 L, and the center of mass of the rod-sphere system is located a distance 3 over 4 L from the axle, as shown in Figure 2.

The rotational inertia of a rod about one of its ends is 1 third m l squared. The rotational inertia of a solid sphere about its center is 2 over 5 m r squared.

Derive an expression for the rotational inertia of the rod-sphere system in terms of M and R. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

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