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. Determine the tangential acceleration of the point that is 0.2 m from the center.

The tangential acceleration is 0 m/s².

Explanation:

Given:

Radius of the wheel = 0.5 m

The point of observation for calculating tangential acceleration = 0.2 m from center.

Tangential speed at the point of observation = 2 m/s

The angular speed of the wheel is a constant.

In order to determine the tangential acceleration, we make use of the following formula:

Tangential acceleration at a point = Angular acceleration × Distance of the point from center

Or,

Now, angular acceleration is defined as the rate of change of angular speed.

Here, the angular speed of the wheel is a constant. So, the change of angular speed is 0. Therefore, the angular acceleration is also 0 rad/s².

Now, from the above formula, as angular acceleration is 0, the magnitude of tangential acceleration at a point that is 0.2 m from the center of the wheel is also 0 m/s².

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.