How Can I Solve These Rotational Kinematics Problems?

In summary: A fan blade whose angular acceleration is a constant 2.00 rad/s^2 rotates through an angle of 285 radians in 11.0s. How long did it take the blade starting from rest to reach the beginning of the 11.0s interval?Answer: 7.45s In summary, the conversation discusses two rotational kinematics problems and the need for assistance in solving them. The first problem involves a spinning wheel and its angular acceleration, final angular velocity, and angular displacement, with the question asking for the time required for the change in angular velocity to occur. The second problem involves a fan blade and its angular acceleration, angle of rotation, and time interval, with the question asking for the time
  • #1
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Rotational Kinematics HELP!?

I desperately need help with two rotational kinematics problems. I do not know what to do in both cases. If someone could be kind enough to go through a solution for me to see it would be very helpful in understanding the problem. Please try and be detailed in your answer as I really want to understand how it is solved.

Homework Statement

1) A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.00rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -25.0rad/s. While this change occurs, the angular displacement of the wheel is zero. Find the time required for the change in the angular velocity to occur.
Answer: 12.5s

2) A fan blade whose angular acceleration is a constant 2.00 rad/s^2 rotates through an angle of 285 radians in 11.0s. How long did it take the blade starting from rest to reach the beginning of the 11.0s interval?
Answer: 7.45s

Homework Equations


Newtonian rotatational formulae.

The Attempt at a Solution


no idea i did the last 20 problems no problems but these 2 are stumping me.
 
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  • #3
These hints should be enough:

1).negative acceleration means deceleration.
zero angular displacement means one complete revolution.
counter clockwise is positive direction.

2).2 pi radian = 1 revolution.
calculate the distance traversed in the desired time interval.
 
  • #4
1) A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.00rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -25.0rad/s. While this change occurs, the angular displacement of the wheel is zero. Find the time required for the change in the angular velocity to occur.
Answer: 12.5s
I don't see how there's enough information there to answer the question. Specifically, what is the initial angular velocity?
 

1. What is rotational kinematics?

Rotational kinematics is the study of the motion of objects that are rotating or moving in a circular path. This branch of physics deals with the concepts of angular displacement, velocity, and acceleration.

2. How is rotational kinematics different from linear kinematics?

Rotational kinematics differs from linear kinematics in that it deals with the motion of objects around a fixed point or axis, while linear kinematics deals with the motion of objects in a straight line.

3. What is angular velocity and how is it calculated?

Angular velocity is the rate at which an object rotates or moves in a circular path. It is calculated by dividing the change in angular displacement by the change in time.

4. Can rotational kinematics be applied to real-life situations?

Yes, rotational kinematics can be applied to real-life situations such as the motion of planets around the sun, the rotation of tires on a car, and the spinning of a top.

5. What is the importance of understanding rotational kinematics?

Understanding rotational kinematics is important in many fields, including engineering, robotics, and sports. It allows us to analyze and predict the motion of rotating objects, which can help in designing efficient and safe systems and improving performance in various activities.

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