36.2: Problems
( \newcommand{\kernel}{\mathrm{null}\,}\)
Translational Problem
Consider the following translational problem: a body of mass m=3.0 kg is initally at rest; then a force of F=5.0 N is applied to it for time t=7.0 seconds. What is the final velocity v of the body?
Solution. Given the force, we can find the acceleration; knowing the acceleration and time, we can find the velocity. The applicable equations are
F=ma
v=at+v0.
Solving Eq. 36.2.1 for a and substituting into Eq. 36.2.2, we have
v=(Fm)t+v0
Substituting the given values of F,m, and t, and using v0=0, we have
v=(5.0 N3.0 kg)(7.0 s)
or
v=11.67 m/s
Rotational Problem
Now consider the following similar rotational problem, which can be solved using the same method: a body of moment of inertia I=3.0 kg m2 is initially at rest (not rotating); then a torque of τ=5.0 N m is applied to it for time t=7.0 seconds. What is the final angular velocity ω of the body?
Solution. Given the torque, we can find the angular acceleration; knowing the angular acceleration and time, we can find the angular velocity. The applicable equations are analogous to those used for the translational problem:
τ=Iα
ω=αt+ω0.
Solving Eq. 36.2.6 for α and substituting into Eq. 36.2.7, we have
ω=(τI)t+ω0
Substituting the given values of τ,I, and t, and using ω0=0, we have
ω=(5.0 N m3.0 kg m)(7.0 s)
or
ω=11.67rad/s