The linear velocity of a particular moving in a circle of radius 30 mathrm(~cm) is 20 mathrm(~km) / mathrm(hr) . If the particle rotates for 3.5 mathrm(sec) , find it, (a) Angular Velocity (b) Angular acceleration (c) angular displacement (d) arc length

(a) Angular Velocity:Angular velocity is defined as the rate of change of angular displacement. It can be calculated using the formula:Angular Velocity ( ) = Linear Velocity ( ) / Radius ( )Given that the linear velocity is and the radius is , we need to convert the units of linear velocity to before calculating the angular velocity. Now, we can calculate the angular velocity: Therefore, the angular velocity is .(b) Angular acceleration:Angular acceleration is the rate of change of angular velocity. It can be calculated using the formula:Angular Acceleration ( ) = Change in Angular Velocity ( ) / Time ( )Since the particle is rotating for , we need to calculate the change in angular velocity first. Given that the initial angular velocity ( ) is 0 (since the particle starts from rest), the change in angular velocity is equal to the angular velocity. Now, we can calculate the angular acceleration: Therefore, the angular acceleration is .(c) Angular displacement:Angular displacement is the product of angular velocity and time. It can be calculated using the formula:Angular Displacement ( ) = Angular Velocity ( ) × Time ( )Given that the angular velocity is and the time is , we can calculate the angular displacement: Therefore, the angular displacement is .(d) Arc length:Arc length is the product of radius and angular displacement. It can be calculated using the formula:Arc Length ( ) = Radius ( ) × Angular Displacement ( )Given that the radius is and the angular displacement is , we can calculate the arc length: Therefore, the arc length is .