Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Physics LibreTexts

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


36.2: Problems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

Support Center

How can we help?