practice problem 1
- the average translational acceleration,
- the average angular acceleration (in radians per second squared), and
- the final angular velocity (in rotations per second)
Review basic problem solving techniques. List the relevant known quantities and the identify the goal of the problem.
∆s = 510 mm = 0.510 m v0 = 0 m/s v = 950 m/s a = ?
Select an appropriate equation. Substitute values and solve for the unknown quantity. (Watch the units.)
v2 = v02 + 2a∆s a = v2 2∆s a = (950 m/s)2 2(0.510 m) a = 8.8 x105 m/s2
This part of the problem is similar in style to the previous part, but slightly more difficult since less is known. We don't have enough information "as is" to solve it. Something else is needed and that something else is time. There are several ways to find it, but my personal choice is to use the two average velocity formulas.
v = ∆s = v + v0 ∆t 2
Rearrange it to make time the subject.
∆t = 2∆s v + v0 ∆t = 2 (0.510 m) 950 m/s + 0 m/s ∆t = 0.001074 s
All that remains now is to select an appropriate equation, substitute, and solve. (Once again, watch the units.)
θ = 2.5 rotations = 5π rad ω0 = 0 rad/s ∆t = 0.001074 s α = ? θ = ω0t + 1 α∆t2 2 α = 2θ ∆t2 α = 2(5π rad) (0.001074 s)2 α = 2.7 × 107 rad/s2
Givens, unknown, equation, substitute, solve. (Watch the units.)
∆t = 0.001074 s α = 2.7 × 107 rad/s2 ω0 = 0 rad/s ω = ? ω = ω0 + α∆t ω = 0 rad/s + (2.7 × 107 rad/s2)(0.001074 s) ω = 29,000 rad/s ω = 4700 rotations per second
practice problem 2
practice problem 3
practice problem 4