a fly wheel turns at 480rpm ,compute the angular speed at any point on the wheel and the tangential speed 30.0cm from the centre .
To compute the angular speed at any point on the wheel, we can use the relationship between angular speed, linear speed, and radius:
Angular speed (ω) = Linear speed (v) / Radius (r)
Given:
Rotations per minute (rpm) = 480
Radius (r) = 30.0 cm
First, we need to convert the rotations per minute to radians per second. Since there are 2π radians in one revolution, we can use the following conversion factor:
1 revolution = 2π radians
Since there are 60 seconds in one minute, we can convert rpm to radians per second as follows:
Angular speed (ω) = 480 rpm * 2π radians / 1 revolution * 1 minute / 60 seconds
Simplifying this expression, we have:
Angular speed (ω) = (480 * 2π) / 60 radians per second
Next, we can calculate the angular speed:
ω = (480 * 2π) / 60
= 32π radians per second
To find the tangential speed 30.0 cm from the centre, we can use the following formula:
Tangential speed (v) = Angular speed (ω) * Radius (r)
Substituting the values we have:
Tangential speed (v) = 32π * 30.0 cm
Simplifying this expression, we have:
Tangential speed (v) = 960π cm per second
So, the angular speed at any point on the wheel is 32π radians per second, and the tangential speed 30.0 cm from the center is 960π cm per second.
To compute the angular speed at any point on the flywheel, we need to recall the relationship between angular speed and rotational speed.
Angular speed (ω) is the rate at which an object rotates around an axis, and it is measured in radians per second (rad/s).
Rotational speed (RPM) is the number of complete rotations an object makes in one minute, and it is measured in revolutions per minute.
We can convert from RPM to rad/s using the following formula:
ω = (2π * RPM) / 60
Given that the flywheel turns at 480 RPM, we can calculate the angular speed as follows:
ω = (2π * 480) / 60
= (2 * 3.1416 * 480) / 60
= (3015.928) / 60
= 50.265 rad/s
Therefore, the angular speed of the flywheel at any point is 50.265 rad/s.
To compute the tangential speed at a specific distance from the center of the flywheel, we can use the formula:
v = r * ω
where:
v is the tangential speed,
r is the distance from the center, and
ω is the angular speed.
Given that the distance from the center is 30.0 cm (or 0.3 m), and the angular speed is 50.265 rad/s, we can calculate the tangential speed as follows:
v = 0.3 * 50.265
= 15.0795 m/s
Therefore, the tangential speed 30.0 cm from the center of the flywheel is 15.0795 m/s.
I dont get this solution
ω = 480 rpm * 2πrad/rev = 960π radians/min
Since s = rθ, tangential speed at r=30 is v=30ω cm/min