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.
The tangential speed of an object moving in a circle can be calculated using the formula:
Tangential speed = Radius × Angular speed
Given:
Radius of the circle (r) = 0.82 m
Angular speed (ω) = 0.25 rev/s
Substituting the values into the formula, we can calculate the tangential speed:
Tangential speed = 0.82 m × 0.25 rev/s
We need to convert revolutions to radians since the angular speed is in revolutions. There are 2π radians in one revolution.
1 revolution = 2π radians
Converting angular speed to radians:
0.25 rev/s = 0.25 rev/s × 2π rad/rev
Tangential speed = 0.82 m × (0.25 rev/s × 2π rad/rev)
Now we can calculate the tangential speed:
Tangential speed ≈ 0.82 m × 1.57 rad/s
Tangential speed ≈ 1.286 m/s
Therefore, the tangential speed of the ball is approximately 1.286 m/s.
To find the tangential speed of the ball, we need to use the formula:
v = r * ω
Where:
- v is the tangential speed,
- r is the radius of the circle,
- ω is the angular speed.
In this case, the radius (r) is given as 0.82 m, and the angular speed (ω) is given as 0.25 rev/s.
Now, let's substitute these values into the formula:
v = 0.82 m * 0.25 rev/s
To get the answer in m/s, we need to convert the angular speed from revolutions per second to radians per second. Since one revolution is equal to 2π radians, we can multiply the angular speed by 2π:
v = 0.82 m * (0.25 rev/s * 2π rad/rev)
Now we can calculate the tangential speed:
v = 0.82 m * (0.5π rad/s)
Simplifying the expression:
v = 0.41π m/s
Using the value of π = 3.14, we can calculate the result:
v = 0.41 * 3.14 m/s
Therefore, the tangential speed of the ball is approximately 1.286 m/s.