An athlete throws a discus from rest to a final angular...

An athlete throws a discus from rest to a final angular velocity of $15 \mathrm{rad} \mathrm{s}^{-1}$ in $0.270 \mathrm{~s}$ before releasing it. During acceleration, discus moves a circular arc of radius $0.810 \mathrm{~m}$. Acceleration of discus before it is $\begin{array}{ll}\text { released is } \\ -2 & \text { (b) } 182 \mathrm{~ms}^{-2}\end{array}$ (a) $45 \mathrm{~m} \mathrm{~s}^{-2}$ (d) $192 \mathrm{~m} \mathrm{~s}^{-2}$ (c) $187 \mathrm{~m} \mathrm{~s}^{-2}$

An athlete throws a discus from rest to a final angular velocity of $15 \mathrm{rad} \mathrm{s}^{-1}$ in $0.270 \mathrm{~s}$ before releasing it. During acceleration, discus moves a circular arc of radius $0.810 \mathrm{~m}$. Acceleration of discus before it is
$\begin{array}{ll}\text { released is } \\ -2 & \text { (b) } 182 \mathrm{~ms}^{-2}\end{array}$
(a) $45 \mathrm{~m} \mathrm{~s}^{-2}$
(d) $192 \mathrm{~m} \mathrm{~s}^{-2}$
(c) $187 \mathrm{~m} \mathrm{~s}^{-2}$

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Key Concepts

Angular Kinematics

Angular kinematics involves the description of rotational motion using quantities such as angular displacement, angular velocity, and angular acceleration. It uses equations analogous to linear motion (such as ? = ?? + ?t and ? = ??t + 0.5?t²) to predict and analyze how objects rotate under constant or variable angular acceleration.

Angular Acceleration

Angular acceleration is the rate of change of angular velocity with respect to time. It is determined by the difference in angular velocities over a given time interval and is a central concept in problems involving objects that speed up or slow down as they rotate.

Tangential Acceleration

Tangential acceleration refers to the acceleration experienced by an object moving along a circular path due to its change in speed along the curve. It is directly related to angular acceleration by the relation a? = r·?, allowing one to convert rotational motion parameters into linear acceleration along the tangential direction.

Circular Motion

Circular motion describes the movement of an object along a circular path, characterized by a constant radius. The relationship between angular displacement and linear displacement is given by s = r?, which bridges the concepts of rotational dynamics and linear kinematics, essential for understanding motion along an arc.

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