a flywheel makes300.rpm. find the angular speed of any point on the wheel and the linear speed(tangential) of a point 5.00m from the center.
V = 300rev/min * 6.28rad/rev * 1min/60s
= 31.4 rad/s.
Circumference = pi*2r = 3.14 * 10=31.4 m.
V = 300rev/min * 31.4m/rev * 1min/60s =
157 m/s. = Linear speed.
To find the angular speed of any point on the wheel, you need to convert the rotation rate in RPM (revolutions per minute) to radians per second.
Step 1: Convert RPM to radians per second
1 revolution = 2π radians
1 minute = 60 seconds
angular speed (in radians per second) = (300 RPM) * (2π radians / 1 revolution) * (1 minute / 60 seconds)
angular speed = 300 * 2π / 60 radians per second
Now, let's calculate the tangential linear speed of a point 5.00m from the center.
Step 2: Calculate tangential linear speed
Tangential linear speed is given by the formula:
linear speed (tangential) = (angular speed) * (radius)
Given:
radius = 5.00m
angular speed = 300 * 2π / 60 radians per second
linear speed (tangential) = (300 * 2π / 60) * (5.00)
Finally, calculate the values:
angular speed ≈ 31.42 radians per second
linear speed (tangential) ≈ 78.54 m/s
Therefore, the angular speed of any point on the wheel is approximately 31.42 radians per second, and the linear speed (tangential) of a point 5.00m from the center is approximately 78.54 m/s.
To find the angular speed of any point on the wheel, we can use the formula:
Angular speed (ω) = RPM × 2π/60
Given that the flywheel makes 300 RPM, we can substitute this value into the formula:
ω = 300 × 2π/60
Next, let's calculate the angular speed:
ω = 10π rad/s
So, the angular speed of any point on the wheel is 10π rad/s.
To find the linear speed (tangential speed) of a point 5.00 m from the center, we can use the formula:
Linear speed (v) = ω × r
Where:
ω is the angular speed in rad/s
r is the distance from the center in meters
Given that the distance from the center is 5.00 m, and the angular speed is 10π rad/s, we can substitute these values into the formula:
v = (10π rad/s) × (5.00 m)
Next, let's calculate the linear speed:
v = 50π m/s
So, the linear speed (tangential speed) of a point 5.00 m from the center is 50π m/s.