What is a tire's angular acceleration if the tangential acceleration at a radius of 0.15 m is 9.4 x 10-2 m/s2?
To find the tire's angular acceleration, we can use the relationship between linear acceleration (tangential acceleration) and angular acceleration. Here are the steps to get the answer:
1. Recall the formula for linear acceleration (tangential acceleration) in terms of angular acceleration and radius:
a = α * r
Where:
a is the linear acceleration (tangential acceleration),
α is the angular acceleration
r is the radius.
2. Plug in the given values into the formula:
a = 9.4 x 10^(-2) m/s^2 (given tangential acceleration)
r = 0.15 m (given radius)
The equation becomes:
9.4 x 10^(-2) m/s^2 = α * 0.15 m
3. Solve for α (angular acceleration):
Divide both sides of the equation by 0.15:
α = (9.4 x 10^(-2) m/s^2) / (0.15 m)
4. Calculate the value:
α = 6.27 rad/s^2
Therefore, the tire's angular acceleration is 6.27 rad/s^2.