The length of the seconds hand of a watch is 10 mm. What is the change in at after 15 seconds (

step 1 So angular speed of angular speed of seconds hand of watch is constant and is constant and equal

The length of the seconds hand of a watch is 10 mm. What is...

The length of the seconds hand of a watch is $10 \mathrm{~mm}$. What is the change in at
after 15 seconds
(a) Zero
(b) $(10 \pi / 2) \mathrm{mms}^{-1}$
(c) $(20 / \pi) \mathrm{mms}^{-1}$
(d) $10 \sqrt{2} \mathrm{mms}^{-1}$

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Key Concepts

Tangential Acceleration

Tangential acceleration refers to the component of acceleration that results in a change in the magnitude of the velocity. In uniform circular motion, since the speed remains constant, the tangential acceleration is zero. This is a crucial concept in understanding why, even though the direction of the velocity changes, there is no acceleration component along the path of the motion.

Angular Displacement

Angular displacement is the measure of the angle through which an object has rotated over a period of time. In the context of circular motion problems, calculating the angular displacement helps determine how the direction of vectors (such as velocity or centripetal acceleration) has changed. It is particularly important in analyzing the changes in the orientation of these vectors over time.

Uniform Circular Motion

Uniform circular motion involves an object moving in a circular path at a constant speed. Although the speed remains unchanged, the direction of the velocity continuously varies, which causes an inward (centripetal) acceleration. This concept is key because it distinguishes between changes in speed (tangential acceleration) and changes in direction (normal acceleration).

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