Let's analyze the problem carefully. ### Given Data: - Initial angular velocity, \(\omega_ 50\, \text{rad/sec}\) - Angular displacement, \(\Delta \theta = 22^\circ \) - The motor \(M\) causes rotation, and the gear \(B\) is attached to the shaft. - Gear ratio related to the gear's radius: \( R_A = 24\, \text{mm} \), \( R_B = 60\, \text{mm} \) --- ### Step 1: Convert angular displacement to radians \[ \Delta \theta = 22^\circ \times \frac{\pi}{180^\circ} = \frac{22\pi}{180} = \frac{\pi}{8.18} \approx .3817\, \text{rad} \] ### Step 2: Find the gear ratio The gear ratio \( G \) relates the angular velocities: \[ \frac{\omega_B}{\omega_A} = \frac{R_A}{R_B} \] or equivalently, the gear ratio for angular velocities is: \[ G = \frac{R_B}{R_A} = \frac{60\, \text{mm}}{24\, \text{mm}} = 2.5 \] ### Step 3: Determine the angular velocity of gear \(B\) Since gear \(A\) is driven by the motor at \(\omega_A = 50\, \text{rad/sec}\), the gear \(B\) will have: \[ \omega_B = \omega_A \times G = 50 \times 2.5 = 125\, \text{rad/sec} \] ### Step 4: Find the angular velocity of the shaft after the displacement The angular velocity of gear \(B\) (which is connected to the shaft in question) is \(125\, \text{rad/sec}\). --- ### **Answer:** \[ \boxed{ \omega_B = 125\, \text{rad/sec} } \]