Verified Answer :
The speed of the bug at the rim of the circular disk is \(\boxed{1\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-
ulldelimiterspace} {\text{s}}}}\) and the acceleration of the bug is \(\boxed{10\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {{{\text{s}}^{\text{2}}}}}} \right.\kern-
ulldelimiterspace} {{{\text{s}}^{\text{2}}}}}}\).
Further Explanation:
Given:
The angular velocity of the disk is \(10\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-
ulldelimiterspace} {\text{s}}}\).
The radius of the circular disk is \(0.1\,{\text{m}}\).
Concept:
The linear speed of the bug present at the rim of the circular disk is given by.
\(v = r \times \omega\)
Here, \(v\) is the linear speed,\(r\) is the radius of the disk and \(\omega\) is the angular speed of the disk.
Substitute \(0.1\,{\text{m}}\) for \(r\) and \(10\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right.\kern-
ulldelimiterspace} {\text{s}}}\) for \(\omega\) in above expression.
\(\begin{aligned}v &= 0.1\,{\text{m}} \times 10\,{{{\text{rad}}} \mathord{\left/{\vphantom {{{\text{rad}}} {\text{s}}}} \right. \kern-
ulldelimiterspace} {\text{s}}} \\&= 1\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-
ulldelimiterspace} {\text{s}}} \\\end{aligned}\)
The magnitude of the centripetal acceleration of the bug cling to the rim of the disk is given as.
\({a_c} = \dfrac{{{v^2}}}{r}\)
Substitute \(1\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-
ulldelimiterspace} {\text{s}}}\) for \(v\) and \(0.1\,{\text{m}}\) for \(r\) in above equation.
\(\begin{aligned}a_c&=\dfrac{(1\text{m/s})^2}{0.1\text{m}}\\&=\frac{1}{0.1}\text{m/s}^2\\&=10\,\text{m/s}^2\end{aligned}\)
Thus, the speed of the bug at the rim of the circular disk is \(\boxed{1\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-
ulldelimiterspace} {\text{s}}}}\) and the acceleration of the bug is \(\boxed{10\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {{{\text{s}}^{\text{2}}}}}} \right.\kern-
ulldelimiterspace} {{{\text{s}}^{\text{2}}}}}}\).
Learn More:
- For typical rubber-on-concrete friction, what is the shortest time in which a car could accelerate from 0 to 80 mph https://brainly.com/question/7174363
- Max and Maya are riding on a merry-go-round that rotates at a constant speed. If the merry-go-round makes 3.5 revolutions in 9.2 seconds https://brainly.com/question/8444623
- Which of the following are units for expressing rotational velocity, commonly denoted by ω https://brainly.com/question/2887706
Answer Details:
Grade: College
Chapter: Uniform Circular motion
Subject: Physics
Keywords: Circular disk, circular motion, angular speed, linear speed, bug clinging, rim of the disk, acceleration, magnitude, constant, rad/s.