Rotational Motion of a wheel turning

In summary, to find the time it takes for a wheel to turn through 60 revolutions at an acceleration of 1.2 rad/s² counterclockwise, we can use the formula ω²=ω₀²+2αθ, where ω₀ is the initial angular velocity (0 rad/s), α is the angular acceleration (1.2 rad/s²), and θ is the angular displacement (60 rev converted to radians). Once we have found the time, we can use the formula ω=Δθ/ΔT to find the rotational speed at that time. It is recommended to use radians instead of revolutions for consistency in units.
  • #1
Falinox
11
0

Homework Statement


A wheel starting from rest accelerates at 1.2 rad/s² counterclockwise.
A) How long does it take to turn through 60 revolutions?
B)What is the rotational speed at that time?

2. The attempt at a solution

I converted 1.2rad/s² to 1.885 rev/s² by dividing by 2πrad (2 pi radians).
So where can I go from here?

Once I find the time in part A I can use the fact that ω=Δθ/ΔT to find the "rotational speed" correct?
 
Physics news on Phys.org
  • #2
Welcome to PF!

Hi Falinox! Welcome to PF! :wink:
Falinox said:
I converted 1.2rad/s² to 1.885 rev/s² by dividing by 2πrad (2 pi radians).
So where can I go from here?

Once I find the time in part A I can use the fact that ω=Δθ/ΔT to find the "rotational speed" correct?

(btw, always leave a space between the number and the unit)

No, you need to use the standard constant acceleration equations, using angular displacement speed and acceleration instead of the linear versions. :smile:
 
  • #3
and i suggest you use radians rather than revolutions; the equations look much nicer that way.
 
  • #4


tiny-tim said:
Hi Falinox! Welcome to PF! :wink:(btw, always leave a space between the number and the unit)

No, you need to use the standard constant acceleration equations, using angular displacement speed and acceleration instead of the linear versions. :smile:

Thanks for the reply!

ω²=ω₀²+2αθ
Given: ω₀=0 rad/s, α=1.2 rad/s²

Is θ my 60 rev? (maybe convert 60 rev to rad?)
 
  • #5
that is the right idea, and yes, theta=60rev, but make sure your units all match before plugging things in. your formula is only true if you use radians, so i would recommend that.
 

1. How does a wheel turn?

A wheel turns by rotating around its axis, which is the imaginary line passing through its center. This rotational motion is caused by a force applied to the wheel, such as pushing or pulling on it.

2. What is the difference between angular velocity and linear velocity?

Angular velocity is the rate of change of an object's angular position, while linear velocity is the rate of change of an object's linear position. In other words, angular velocity describes how fast an object is rotating, while linear velocity describes how fast an object is moving in a straight line.

3. How is torque related to rotational motion of a wheel?

Torque is the force that causes an object to rotate. In the case of a wheel turning, torque is applied to the wheel by the force exerted on it, causing it to rotate around its axis. The greater the torque applied, the faster the wheel will rotate.

4. Can a wheel turn without any external force?

No, a wheel cannot turn without any external force. According to Newton's first law of motion, an object will remain at rest or in motion at a constant speed in a straight line unless acted upon by an external force. In the case of a wheel, an external force must be applied to cause it to rotate.

5. How does the shape of a wheel affect its rotational motion?

The shape of a wheel can affect its rotational motion in several ways. For example, a larger wheel will have a greater rotational inertia, meaning it will require more torque to start and stop its rotation. Additionally, the shape of the wheel's tread can impact its grip and traction, affecting its ability to turn smoothly and efficiently.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
407
Replies
12
Views
629
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
158
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
966
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
232
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
32
Views
1K
Back
Top