1.A flywheel is rotating at 7 rad/sec. It has a 15-cm diameter. What is the speed of a point on its rim, in cm/min?
2.A wheel is rotating at 3 radians/sec. The wheel has a 30 cm radius. What is the speed of a point on its rim, in m/min?
3.What is the angular speed in radians/second associated with a rotating an angle 3pi/4 radians in 2 seconds?
second one???
1. R = 7.5 cm
omega = 7 rad/s
v = omega R = 7*7.5 cm/s
= 52.5 cm/s
53.5 cm/s * 60 s/min = 3150 cm/min
2. D = .30 meters
R = .15 meter
omega = 3 rad/s * 60 s/min = 180 rad / min
v = omega * R = .15 meter *180 rad/min = .15 * 180 meters/minute
3. oh come on
3 pi/8 radians/second
1. The speed of a point on the rim of the flywheel can be calculated using the formula: speed = radius x angular speed. Since the diameter is given, we need to convert it to radius by dividing it by 2.
Radius = Diameter/2 = 15 cm/2 = 7.5 cm
Now, we can calculate the speed using the formula:
Speed = Radius x Angular Speed
= 7.5 cm x 7 rad/sec = 52.5 cm/sec
To convert it to cm/min, we can multiply it by 60:
Speed = 52.5 cm/sec x 60 sec/min = 3150 cm/min
So, the speed of a point on the rim of the flywheel is 3150 cm/min.
2. Similar to the previous question, we can use the formula: speed = radius x angular speed.
Radius = 30 cm
Now, we can calculate the speed using the formula:
Speed = Radius x Angular Speed
= 30 cm x 3 rad/sec = 90 cm/sec
To convert it to m/min, we need to divide it by 100:
Speed = 90 cm/sec / 100 = 0.9 m/sec
Now, to convert it to m/min, we multiply by 60:
Speed = 0.9 m/sec x 60 sec/min = 54 m/min
So, the speed of a point on the rim of the wheel is 54 m/min.
3. To find the angular speed in radians/second associated with a rotating angle of 3pi/4 radians in 2 seconds, we divide the angle by the time:
Angular speed = Angle / Time
= (3pi/4 radians) / 2 seconds
= 3pi/8 radians per second
So, the angular speed associated with rotating an angle of 3pi/4 radians in 2 seconds is 3pi/8 radians per second.
1. To find the speed of a point on the rim of the flywheel in cm/min, we need to convert the angular velocity from rad/sec to cm/min.
First, let's calculate the circumference of the flywheel using its diameter. The diameter is given as 15 cm, so the radius is half of that, which is 7.5 cm. The circumference of the flywheel is equal to 2π times the radius.
Circumference = 2π * radius
Circumference = 2π * 7.5 cm
Circumference ≈ 47.12 cm
Next, let's convert the angular velocity from rad/sec to cm/min. We know that 1 revolution is equal to 2π radians.
Angular velocity in cm/min = (Angular velocity in rad/sec) * (Circumference in cm / 2π radians)
Angular velocity in cm/min = 7 rad/sec * (47.12 cm / 2π radians)
Angular velocity in cm/min ≈ 111.86 cm/min
Therefore, the speed of a point on the rim of the flywheel is approximately 111.86 cm/min.
2. To find the speed of a point on the rim of the wheel in m/min, we need to convert the angular velocity from rad/sec to m/min.
First, let's calculate the circumference of the wheel using its radius. The radius is given as 30 cm. The circumference of the wheel is equal to 2π times the radius.
Circumference = 2π * radius
Circumference = 2π * 30 cm
Circumference ≈ 188.5 cm
Next, let's convert the angular velocity from rad/sec to m/min. We know that 1 revolution is equal to 2π radians, and 1 meter is equal to 100 cm.
Angular velocity in m/min = (Angular velocity in rad/sec) * ((Circumference in cm / 100 cm) / 2π radians)
Angular velocity in m/min = 3 rad/sec * (188.5 cm / 100 cm / 2π radians)
Angular velocity in m/min ≈ 2.83 m/min
Therefore, the speed of a point on the rim of the wheel is approximately 2.83 m/min.
3. To find the angular speed in radians/second associated with rotating an angle of 3π/4 radians in 2 seconds, we need to divide the angle by the time.
Angular speed in radians/second = (Angle in radians) / (Time in seconds)
Angular speed in radians/second = (3π/4) radians / 2 seconds
Angular speed in radians/second = (3π/4) / 2 radians/second
Angular speed in radians/second = (3π/4) * (1/2) radians/second
Angular speed in radians/second = 3π/8 radians/second
Therefore, the angular speed in radians/second associated with rotating an angle of 3π/4 radians in 2 seconds is 3π/8 radians/second.
1. To find the speed of a point on the rim of a rotating flywheel, we need to convert the angular speed from radians per second to radians per minute. Then, we can use the formula for the circumference of a circle to calculate the speed.
First, let's convert the angular speed from radians per second to radians per minute:
7 rad/sec * 60 sec/min = 420 rad/min
Next, we need to find the circumference of the flywheel. The diameter is given as 15 cm, so the radius is half of that, which is 7.5 cm. The formula for the circumference of a circle is C = 2πr, where r is the radius:
C = 2 * 3.14 * 7.5 cm = 47.1 cm
Finally, we can calculate the speed of a point on the rim by multiplying the angular speed by the circumference of the flywheel:
Speed = 420 rad/min * 47.1 cm/rad ≈ 19,782 cm/min
Therefore, the speed of a point on the rim of the flywheel is approximately 19,782 cm/min.
2. Similar to the first question, to find the speed of a point on the rim of a rotating wheel, we need to convert the angular speed from radians per second to radians per minute. Then, we can use the formula for the circumference of a circle to calculate the speed.
First, let's convert the angular speed from radians per second to radians per minute:
3 rad/sec * 60 sec/min = 180 rad/min
Next, we need to find the circumference of the wheel. The radius is given as 30 cm. The formula for the circumference of a circle is C = 2πr, where r is the radius:
C = 2 * 3.14 * 30 cm = 188.4 cm
Finally, we can calculate the speed of a point on the rim by multiplying the angular speed by the circumference of the wheel:
Speed = 180 rad/min * 188.4 cm/rad = 34,032 cm/min
Therefore, the speed of a point on the rim of the wheel is 34,032 cm/min or approximately 340.32 m/min.
3. Angular speed is defined as the change in angular displacement divided by the change in time. Therefore, to calculate the angular speed, we need to divide the change in angle by the time taken.
The given angle is 3π/4 radians, and the time taken is 2 seconds. To find the angular speed, we divide the angle by the time:
Angular speed = (3π/4 radians) / 2 seconds
To calculate this, we can divide 3π/4 by 2:
Angular speed = (3π/4) / 2 = 3π/8 radians per second
Therefore, the angular speed associated with rotating an angle of 3π/4 radians in 2 seconds is 3π/8 radians per second.