---
title: "A 6.0-cm-diameter gear rotates with angular velocity [katex] w= \\left(20-\\frac {1}{2} t^2 \\right) \\text {rad}{s}[\\katex], where t is in seconds. At t= 4.0 s, what are:"
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url: "https://nerd-notes.com/ubq/39109/"
date_modified: "2024-09-07T11:57:49+00:00"
---

# A 6.0-cm-diameter gear rotates with angular velocity [katex] w= \left(20-\frac {1}{2} t^2 \right) \text {rad}{s}[\katex], where t is in seconds. At t= 4.0 s, what are:

A 6.0-cm-diameter gear rotates with angular velocity \( \omega = \left(20-\frac {1}{2} t^2 \right) \, \text {rad/s} \), where \(t\) is in seconds. At \(t = 4.0 \, \text{s}\), what are

**Part a)** The gear’s angular acceleration? Hint: Use a graph if you haven’t learned calculus yet. *(3 points)*

**Part b)** The tangential acceleration of a tooth on the gear? *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/39109/*