An athlete swings a 2.01 kg ball horizontally
on the end of a rope. The ball moves in a
circle of radius 0.98 m at an angular speed of
0.44 rev/s.
What is the tangential speed of the ball?
Answer in units of m/s.
C = pi*2r = 3.14 * 2*0.98 = 6.15 m.
0.44rev/s. * 6.15m/rev = 2.71 m/s. = Tangential speed.
To find the tangential speed of the ball, we can use the formula:
tangential speed = radius x angular speed
Given:
Radius (r) = 0.98 m
Angular speed (ω) = 0.44 rev/s
Let's calculate:
tangential speed = 0.98 m x 0.44 rev/s
To convert rev/s to rad/s, we know that 1 revolution = 2π radians.
So, 0.44 rev/s = 0.44 x 2π rad/s
tangential speed = 0.98 m x (0.44 x 2π) rad/s
Calculating the expression inside the parentheses:
tangential speed = 0.98 m x (0.88π) rad/s
Now, we can calculate the exact value:
tangential speed ≈ 2.717 m/s
Therefore, the tangential speed of the ball is approximately 2.717 m/s.
To find the tangential speed of the ball, we need to use the formula:
Tangential speed = radius × angular speed
Given:
Radius (r) = 0.98 m
Angular speed (ω) = 0.44 rev/s
Substituting these values into the formula, we get:
Tangential speed = 0.98 m × 0.44 rev/s
Before we proceed, we need to convert the given angular speed from revolutions per second to radians per second. Since 1 revolution is equivalent to 2π radians, we can multiply the angular speed by 2π to convert it:
Tangential speed = 0.98 m × (0.44 rev/s × 2π rad/rev)
Now, let's calculate the solution step by step:
1. Multiply the angular speed by 2π:
(0.44 rev/s × 2π rad/rev) ≈ 2.76 rad/s
2. Multiply the radius by the angular speed:
0.98 m × 2.76 rad/s ≈ 2.7128 m/s
Therefore, the tangential speed of the ball is approximately 2.7128 m/s.