A model airplane with mass 0.750 kg is tethered to the...

A model airplane with mass $0.750 \mathrm{~kg}$ is tethered to the ground by a wire so that it flies in a horizontal circle $30.0 \mathrm{~m}$ in radius. The airplane engine provides a net thrust of $0.800 \mathrm{~N}$ perpendicular to the tethering wire. (a) Find the torque the net thrust produces about the center of the circle. (b) Find the angular acceleration of the airplane. (c) Find the translational acceleration of the airplane tangent to its flight path.

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Key Concepts

Relation between Angular and Tangential Acceleration

Angular acceleration describes the rate of change of angular velocity in a rotating system, while tangential (linear) acceleration refers to the acceleration along the circular path. They are related by the radius of the circle, with tangential acceleration equal to angular acceleration multiplied by the radius.

Newton's Second Law for Rotation

This law establishes the relationship between net torque, moment of inertia, and angular acceleration, analogous to F = ma in linear dynamics. It is expressed as torque = moment of inertia × angular acceleration and is fundamental to solving problems in rotational dynamics.

Torque

Torque is a measure of the effectiveness of a force in causing an object to rotate about a specific axis. It is defined as the product of the force and the perpendicular distance from the axis (lever arm), and it plays a key role in analyzing rotational motion.

Moment of Inertia

Moment of inertia quantifies how much an object resists rotational acceleration about an axis. It depends on the distribution of mass relative to the axis of rotation, with point masses having an inertia given by the product of their mass and the square of their distance from the axis.

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