Figuring out angular velocity from θ = 2.0 + 4.0t^2 + 2.0t^3

AI Thread Summary
To find the angular velocity from the equation θ = 2.0 + 4.0t² + 2.0t³, differentiate θ with respect to time t, yielding w = dθ/dt = 8.0t + 6.0t². At t = 0, the angular position is 2.0 radians and the angular velocity is 0 rad/s. At t = 4.0 s, the angular velocity can be calculated as w = 8.0(4) + 6.0(4)², resulting in 128 rad/s. The angular acceleration can be determined by differentiating the angular velocity, and it is not constant due to the presence of the t² term in the angular velocity equation. Understanding these calculations is essential for solving the problem accurately.
Stonem42
Messages
1
Reaction score
0

Homework Statement



The angular position of a point on a rotating wheel is given by θ = 2.0 + 4.0t2 + 2.0t3, where θ is in radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 4.0 s? (d) Calculate its angular acceleration at t = 2.0 s. (e) Is its angular acceleration constant?

Homework Equations



w = dθ/dt I am stuck on figuring out how to angular velolcity is:

(8.0rad/s^2)t + (6.0rad/s^3)t^2

as my professor put it, its buggin me how i can't put two and two together.

The Attempt at a Solution

 
Physics news on Phys.org
Stonem42 said:
w = dθ/dt I am stuck on figuring out how to angular velolcity is:

I'm stuck on what you're stuck on. What?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is（Figure 2）： F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Solve Angular Velocity & Acceleration - Dimensional Analysis
Replies
3
Views
2K
Angular velocity- A toy train rolls around a horizontal track
Replies
8
Views
753
Angular Velocity of a Car going around a curve
Replies
9
Views
1K
Help with Angular Velocity True-False Question
Replies
12
Views
1K
Angular velocity and angular acceleration of a turbine
Replies
17
Views
3K
Particle experiencing only an angular force, determine the r dot
Replies
15
Views
2K
The final velocity of a ball rolling while slipping.
Replies
40
Views
4K
Angular Velocity and Acceleration
Replies
10
Views
2K
Dynamics of Rotational Motion and hinge
Replies
2
Views
3K
Determine the angular acceleration and angular velocity
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top