Determine the angular velocity in rad/sec of a wheel rotating at 75 in half a min. Leave answer in terms of pi
If that's supposed to be 75 rev in half a minute
ω = 2πr = 2π(75/0.5)ad/min * 1min/60sec = 5π rad/s
To determine the angular velocity in rad/sec, we need to use the formula:
Angular velocity (ω) = (θ / t)
Where:
- θ is the angle covered by the wheel in radians
- t is the time taken in seconds
Given that the wheel rotates 75 times in half a minute, we need to convert the time to seconds:
1 minute = 60 seconds
Half a minute = 60/2 = 30 seconds
Since the wheel makes 75 rotations, we need to find the angle covered in radians:
1 revolution = 2π radians
75 revolutions = 75 * 2π radians = 150π radians
Now we can calculate the angular velocity:
ω = (150π radians) / (30 seconds)
ω = 5π radians/second
So, the angular velocity of the wheel rotating at 75 in half a minute is 5π radians/second.