A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its
center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s.
(a) Determine the tangential speed of a point 0.4 m from the center of the wheel.
(b) Determine the tangential acceleration of the point that is 0.2 m from the center.
You are correct. moment of inertia is not in the picture, acceleration tangential is zero. Good point.
Use the .5m radius to calculate the moment of inertia. Use the radius of .4 (or on b of .2) to find tangential speed (w*r)
What is the role of Moment of inertia here?
Am I right if I say that the tangential speed is the same 2 m/s & the tangential acceleration zero ?
Answer
For this question
To determine the tangential speed of a point 0.4 m from the center of the wheel, we can use the concept of angular velocity.
The angular velocity (ω) of the wheel can be found using the formula:
ω = tangential speed / radius
Given that the point 0.2 m from the center has a tangential speed of 2 m/s, and the radius of the wheel is 0.5 m, we can calculate the angular velocity:
ω = 2 m/s / 0.5 m
ω = 4 rad/s
Now, to determine the tangential speed of a point 0.4 m from the center, we can use the same formula:
tangential speed = ω * radius
Substituting the values, we have:
tangential speed = 4 rad/s * 0.4 m
tangential speed = 1.6 m/s
Therefore, the tangential speed of a point 0.4 m from the center of the wheel is 1.6 m/s.
Moving on to part (b), to determine the tangential acceleration of the point that is 0.2 m from the center, we need to use the concept of tangential acceleration.
The tangential acceleration (at) is given by:
at = radius * angular acceleration
Since we are not given the angular acceleration, we need to use another formula that relates angular acceleration with tangential acceleration:
at = radius * (dω / dt)
Here, (dω / dt) represents the rate of change of angular velocity with time. However, since the problem states that the wheel rotates with a constant angular speed, the angular acceleration is zero (dω / dt = 0).
Therefore, the tangential acceleration of the point that is 0.2 m from the center is also zero.