Calculating tangential acceleration of rotating object

In summary, the problem asks for the average tangential acceleration of the tire of an exercise bicycle, given that an ant on the outer edge of the tire experiences an increase in speed from 0 to 10 m/s in 2.6 seconds, and the wheel's rotational acceleration is 13 rad/s^2. The equations used to solve for the average tangential acceleration include v=ω*r and a=∝*r, but the radius could not be eliminated in these equations. It may be possible to find the radius using the given information. Additionally, other equations such as v=Δx/Δt, a=Δv/Δt, ω=ΔΘ/Δ
  • #1
APphysicsSenior
4
0

Homework Statement


An ant clings to the outside edge of the tire of an exercise bicycle. When you start pedaling, the an't speed increases from ) to 10 m/s in 2.6 s. The wheel's rotational acceleration is 13 rad/s^s.

Determine the average tangential acceleration of the tire.

Homework Equations


v=ω*r
a=∝*r
v=Δx/Δt
a=Δv/Δt
ω=ΔΘ/Δt
∝=Δω/Δt

The Attempt at a Solution


I tried to manipulate the formulas that involved ∝, v and t in order to solve for a, but I couldn't get the radius to cancel out, or I kept ending up with ω in the equation. I need help figuring out how to convert rotational acceleration (∝) to linear acceleration (a) WITHOUT the radius.
 
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  • #2
Maybe you can find the radius from what is already given. Can you find the linear acceleration of the ant from what is given?
 
  • #3
APphysicsSenior said:
That is the "is proportional to" symbol. What you mean is α (alpha).
APphysicsSenior said:
tried to manipulate the formulas
Please post your working. Check whether you used all the given information. If you did not, try to find an equation that involves the information you did not use.
 

Related to Calculating tangential acceleration of rotating object

1. What is tangential acceleration?

Tangential acceleration is the rate of change of an object's tangential velocity as it moves along a circular path. It is a measure of how quickly the direction of an object's velocity is changing.

2. How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula: at = r * α, where at is the tangential acceleration, r is the radius of the circular path, and α is the angular acceleration of the object.

3. What is the difference between tangential acceleration and centripetal acceleration?

Tangential acceleration is the acceleration along the tangent of a circular path, while centripetal acceleration is the acceleration towards the center of the circular path. They are related but distinct concepts.

4. Can tangential acceleration be negative?

Yes, tangential acceleration can be negative if the object is slowing down or changing direction. A negative tangential acceleration indicates that the object is accelerating in the opposite direction of its velocity.

5. How does tangential acceleration affect the motion of a rotating object?

Tangential acceleration affects the speed and direction of a rotating object. A higher tangential acceleration will result in a faster change in speed or direction, while a lower tangential acceleration will result in a slower change.

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