An athlete swings a 3.06 kg ball horizontally on the end of a rope. The ball moves in
a circle of radius 0.82 m at an angular speed
of 0.25 rev/s.
What is the tangential speed of the ball?
Answer in units of m/s
To find the tangential speed of the ball, we can use the formula:
Tangential speed = Radius x Angular speed
Given:
Radius (r) = 0.82 m
Angular speed (ω) = 0.25 rev/s
Plugging in the values, we get:
Tangential speed = 0.82 m x 0.25 rev/s
To convert rev/s to rad/s, we know that 1 revolution is equal to 2π radians.
So, 0.25 rev/s is equivalent to 0.25 x 2π rad/s.
Tangential speed = 0.82 m x 0.25 x 2π rad/s
Now, we can calculate the tangential speed:
Tangential speed = 0.82 m x 0.25 x 2π rad/s
Multiply the numbers together:
Tangential speed = 0.82 m x 0.5π rad/s
Evaluate the multiplication:
Tangential speed ≈ 1.291 m/s
Therefore, the tangential speed of the ball is approximately 1.291 m/s.