please help me to solve this problem:

calculate the angular velocity of a point for the given number of revolutions and time. express the answer on in radians per minute.

1.θ=1/2;t=2min.
2.θ=1/4;t=5min.
3.θ=2/3;t=10min.
4.θ=3/5;t=12min.
5.θ=5/6;t=15min.
6.θ=1/3;t=3min.

1. Va=(1/2)rev/2min * 6.28rad/rev= 1.57

rad/min.

2 through 6. Same procedure as #1.

To calculate the angular velocity of a point, we can use the formula:

Angular velocity = θ / t

where θ is the number of revolutions and t is the time in minutes.

Let's calculate the angular velocity for each given scenario:

1. θ = 1/2; t = 2 min
Angular velocity = (1/2) / 2 = 1/4 radians per minute

2. θ = 1/4; t = 5 min
Angular velocity = (1/4) / 5 = 1/20 radians per minute

3. θ = 2/3; t = 10 min
Angular velocity = (2/3) / 10 = 1/15 radians per minute

4. θ = 3/5; t = 12 min
Angular velocity = (3/5) / 12 = 1/20 radians per minute

5. θ = 5/6; t = 15 min
Angular velocity = (5/6) / 15 = 1/18 radians per minute

6. θ = 1/3; t = 3 min
Angular velocity = (1/3) / 3 = 1/9 radians per minute

Therefore, the angular velocity for each scenario is:

1. 1/4 radians per minute
2. 1/20 radians per minute
3. 1/15 radians per minute
4. 1/20 radians per minute
5. 1/18 radians per minute
6. 1/9 radians per minute

To calculate the angular velocity, we need to use the formula:

Angular velocity (ω) = θ / t

Where:
- ω is the angular velocity in radians per minute
- θ is the number of revolutions
- t is the time in minutes

Let's calculate the angular velocity for each given problem:

1. θ = 1/2; t = 2 min
ω = (1/2) / 2
= 1/4 radians per minute

2. θ = 1/4; t = 5 min
ω = (1/4) / 5
= 1/20 radians per minute

3. θ = 2/3; t = 10 min
ω = (2/3) / 10
= 1/15 radians per minute

4. θ = 3/5; t = 12 min
ω = (3/5) / 12
= 1/20 radians per minute

5. θ = 5/6; t = 15 min
ω = (5/6) / 15
= 1/18 radians per minute

6. θ = 1/3; t = 3 min
ω = (1/3) / 3
= 1/9 radians per minute

So the angular velocity for each problem, expressed in radians per minute, is as follows:

1. ω = 1/4 radians per minute
2. ω = 1/20 radians per minute
3. ω = 1/15 radians per minute
4. ω = 1/20 radians per minute
5. ω = 1/18 radians per minute
6. ω = 1/9 radians per minute