# Angular kinematics question

1. Sep 19, 2009

### Fihzix

1. The problem statement, all variables and given/known data
The angular position of a point on the rim of a 18.7 cm rotating wheel is given by θ(t) = 4.7 t2 − 7.2 t +9.7, where θ is measured in radians and t is measured in seconds.

What is the instantaneous angular acceleration α of the point at time t = 6 s?
What is the instantaneous tangential (not radial!) acceleration a of the point at time t =6 s?
What is the instantaneous angular velocity ω of the point at time t = 9 s?
What is the instantaneous speed v of the point at time t = 9 s?
What is the average angular speed ωav of the point over the time interval starting time t = 6 s and ending at the time t = 9 s?
Through what angular displacement Δθ does the wheel turn during this time?

3. The attempt at a solution
I get the angular position of 135.7 radian at 6 seconds but I do not understand where to go from there. I cannot just use those for angular velocity/acceleration right?

Thanks.

2. Sep 19, 2009

### rl.bhat

If θ is given, how to find the angular velocity and angular acceleration.
Can you find them by differentiating θ(t)
What is relation between linear velocity and angular velocity?

3. Sep 20, 2009

### Fihzix

Sorry, I was just introduced to this and I am super confused.

4. Sep 21, 2009

### rl.bhat

Angular position of the wheel is given as θ(t) = 4.7 t2 − 7.2 t +9.7
The angular velocity = ω = d[θ(t)] /dt
The angular acceleration = α = d(ω)/dt
linear velocity v = ω*R
linear acceleration = a = Rα

5. Sep 21, 2009

### Fihzix

I am able to get the last two questions involving average angular speed and displacement because I can simply plug in the numbers but I don't know how to find the instantaneous values. I know how to find the speed up to that point but not specifically at that instant.

6. Sep 21, 2009

### ace99

hi, i too have a similar question to that, i was able to get the instantaneous angular velocity but doing derivatives then just plugin in the point, but i dont understand how to get the instantaneous angular acceleration and instantaneous tangential acceleration.

7. Sep 21, 2009

### rl.bhat

$$Angular acceleration \alpha = \frac{d^{2}\theta}{dt^{2}}$$

Tangential acceleration = Rα.

8. Sep 21, 2009

### ace99

sorry to be a bother, but i still dont quite understand that formula. is it another derivative?

9. Sep 21, 2009

### rl.bhat

Instantaneous angular velocity ω = dθ/dt
Instantaneous angular acceleration = α = dω/dt

10. Sep 22, 2009

### Fihzix

I am also still confused about that formula. (surprise, surprise)

11. Sep 22, 2009

### rl.bhat

In he problem θ(t) = 4.7*t^2 - 7.2*t + 9.7
Can you find the derivative of θ with respect to t?

12. Sep 22, 2009

### Fihzix

I am still awaiting the derivative lecture in calculus. I expect this is why I am unable to continue in physics.

13. Sep 22, 2009

### rl.bhat

Sorry. Without the knowledge of derivative you cannot solve this problem.

14. Sep 22, 2009

### Fihzix

Thanks for your help, this makes much more sense to me now. I guess I cant do my physics assignment though. haha

15. Sep 22, 2009

### rl.bhat

If you are very much particular about the physics assignment, why can't you open your maths book and go through basic rules of derivative?
Just one rule is sufficient.
If y = x^2, then dy/dx = 2x.
And if y = x, then dy/dx = 1.

16. Sep 22, 2009

### ace99

so whats the rule for d^2y/dx^2?

as in $$Angular acceleration \alpha = \frac{d^{2}\theta}{dt^{2}}$$

17. Sep 22, 2009

### rl.bhat

If θ = t^2
then dθ/dt = 2t
and d^2(θ)/dt^2 = 2