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Physics Chapter: Rotational Dynamics and Inertia

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Physics Chapter: Rotational Dynamics and Inertia

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Questions and Answers

What are the consistent SI units used when working with torque and angular acceleration?

The consistent SI units are: meters (m) for length, radians (rad) for angular displacement, kilograms (kg) for mass, and seconds (s) for time.

What is the formula for calculating the moment of inertia, I, in terms of angular acceleration, a, torque, t, and time t?

I = t/a

What is the moment of inertia of a thin hoop with radius R?

1/12ML²

1/2MR²

MR² (correct)

2/5MR²

Match the following objects to their corresponding moment of inertia formulas:

Thin hoop, radius R = MR² Thin hoop, radius R, width w = 1/2Mw² Solid cylinder, radius R, length l = 1/2MR² Long uniform rod, length l, through the center = 1/12ML² Hollow cylinder, inner radius R1, outer radius R2 = 1/2M(R1² + R2²) Uniform sphere, radius R = 2/5MR² Long uniform rod, length l, through one end = 1/3ML² Rectangular thin plate, length l, width w, through the center = 1/12M(l² + w²) Signup and view all the answers

The moment of inertia always stays the same, regardless of the axis of rotation.

False Signup and view all the answers

What are the two laws used to solve rotational motion problems?

Newton's second law for rotation and Newton's second law for translation Signup and view all the answers

Study Notes

Rotational Dynamics

Using torque and angular acceleration (Eq. 8-14) requires consistent units (SI: N⋅m; rad/s²; kg⋅m²).
Moment of inertia (I) is calculated as I = τ/α, where τ is torque and α is angular acceleration.

Moments of Inertia

Different shapes have distinct moment of inertia formulas.
Thin hoop: I = MR² (axis through center)
Thin hoop: I = MR² (axis through center)
Solid cylinder: I = ½MR² (axis through center)
Hollow cylinder: I = ½M(R₁² + R₂²) (axis through center)
Uniform sphere: I = ⅔MR² (axis through center)
Long uniform rod: I = (1/12)ML² (axis through center)
Long uniform rod: I = (1/3)ML² (axis through end)
Rectangular thin plate: I = (1/12)M(w² + l²) (axis through center)

Solving Rotational Motion Problems

Draw diagrams and choose the system.
Include all forces and their directions, noting the axis of rotation for torque calculation.
Determine torques (positive for counterclockwise).
Use Newton's second law for rotation (∑τ = Iα).
Apply Newton's second law for linear motion (∑F = ma).
Consider consistent units and reasonable answers.

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Description

Test your knowledge of rotational dynamics and moment of inertia in this quiz. It covers essential formulas for calculating torque, angular acceleration, and the moments of inertia for various shapes. Perfect for students studying physics principles related to motion.