Ratio of Angular Speeds in UCM – Rankers Physics

Uncategorized: Practice Problem & Solution

Two particles A and B are moving in uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speed \(v_A\) and \(v_B\) respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be: (2019)
\(r_Atext{ : }r_B\)
\(v_Atext{ : }v_B\)
\(r_Btext{ : }r_A\)
1:1

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Relationship between angular speed and time period in UCM.
Formula: Angular speed \(omega = 2pi / T\).
Given that time period \(Ttext{ is same for both A and B}\).
Therefore, \(omega_A = 2pi / T\) and \(omega_B = 2pi / T\).
Thus, \(omega_A = omega_B\), and the ratio \(omega_A : omega_B = 1:1\).

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