Question

A ball with mass m = 9 g at the end of a massless cord is swinging in a circle of radius R = 1.39 m with and angular velocity ω = 15 rad/s.

Write an expression for the velocity v of the ball.

Answer 1

To find the velocity of a ball swinging in a circle, multiply the angular velocity (ω) by the radius (R) of the circle. With an angular velocity of 15 rad/s and a radius of 1.39 m, the ball's velocity is 20.85 m/s.

Step-by-step explanation:

The question is asking for an expression for the velocity v of a ball swinging in a circle with known mass, radius, and angular velocity. The velocity of an object moving in circular motion can be calculated using the formula v = ω × R, where ω is the angular velocity and R is the radius of the circle. In this scenario, the provided angular velocity is 15 rad/s and the radius is 1.39 m. Multiplying these values will give the tangential velocity of the ball.

To solve for the ball's velocity, the calculation would be v = 15 rad/s × 1.39 m, which results in v = 20.85 m/s. This value represents the linear speed of the ball on its circular path.