A grinding wheel has a radius of 0.30 m at rest and accelerates with a constant angular acceleration of 0.50 rad/s2. What is its tangential acceleration?
Question
A grinding wheel has a radius of 0.30 m at rest and accelerates with a constant angular acceleration of 0.50 rad/s². What is its tangential acceleration?
Solution
The tangential acceleration (a_t) of an object moving in a circle is the linear acceleration along a line tangent to the direction of motion. It can be calculated using the formula:
a_t = r * α
where: r is the radius of the circle, α is the angular acceleration.
Given: r = 0.30 m (radius of the grinding wheel) α = 0.50 rad/s² (angular acceleration)
Substituting the given values into the formula, we get:
a_t = 0.30 m * 0.50 rad/s² = 0.15 m/s²
So, the tangential acceleration of the grinding wheel is 0.15 m/s².
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