Circular motion -- Find the angular velocity at t=3

• jisbon
In summary, The conversation discusses finding the angular velocity by integrating the angular acceleration formula. However, the given answer does not match the calculated result and it is suggested to check the initial angular velocity and the presence of a negative symbol in the tangential acceleration formula.
jisbon
Homework Statement
Consider a object going circular motion of radius 0.14m, angular acceleration is given by a(t) = 2t The tangential velocity at t=0 is 0.5m/s
Find angular velocity at t=3
Relevant Equations
tangential acc = r * angular acc
Hi everyone. Do correct me if I am thinking wrongly.
So to find angular velocity, won't I just have to integrate angular acc = 2t, which means angular velocity = t^2? Hence, won't the answer be 3^2=9?
The answer seems to be 5.43 :/
Thanks

You have ignored the initial angular velocity. ω = ω0 + ∫a(t)dt.
That still doesn't give the given answer. Are you sure the initial tangential velocity wasn't -0.5 m/s? Either you or the book seems to have made a typo.

Figured out the intial angular velocity part.
Regarding the negative, will check back with my tutors. Find it weird too :/

jisbon said:
Figured out the intial angular velocity part.
Regarding the negative, will check back with my tutors. Find it weird too :/
Did you quote it word for word? Was there a diagram?

This part of the question was just added: Assume tangential acc is opposite to tangential velocity, hence the negative

1. What is circular motion?

Circular motion is a type of motion where an object moves in a circular path around a fixed center point. This can occur when there is a force acting on the object towards the center of the circle, such as gravity or tension.

2. How is angular velocity defined?

Angular velocity is the rate at which an object rotates around a fixed point, measured in radians per second. It is calculated by dividing the angle of rotation by the time it takes to complete that rotation.

3. How do you find the angular velocity at a specific time?

To find the angular velocity at a specific time, you will need to know the angle of rotation at that time and the time it took to complete that rotation. You can then use the formula angular velocity = angle of rotation / time to calculate it.

4. What is the unit of measurement for angular velocity?

Angular velocity is typically measured in radians per second (rad/s) or degrees per second (deg/s). Both units represent the rate at which an object is rotating around a fixed point.

5. How does angular velocity relate to linear velocity?

Angular velocity and linear velocity are related through the formula linear velocity = angular velocity x radius. This means that the faster an object is rotating (higher angular velocity), the faster it is also moving along its circular path (higher linear velocity).

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