Answer in Physics for Diocos #172487
During a 7.0-s time interval, a flywheel with a constant angular acceleration turns through 600 radians that acquire an angular velocity of 100 rad/s.
- The angular velocity at the beginning of the 7.0s is _________
- The angular acceleration of the flywheel is ________
1. By definition, the angular acceleration is:
“varepsilon =dfrac{Delta omega }{Delta t}”
where “Delta omega = 100 rad/s” is the gain in angular velocity in time interval “Delta t = 7s”. Thus, obtain:
“varepsilon = dfrac{100rad/s}{7s}approx 14.3space rad/s^2”
2. The number of radians the wheel turned throug is given as follows:
“varphi = omega_0(Delta t) + dfrac{varepsilon(Delta t)^2}{2}”
where “omega _0” is the initial angular velocity. Substituting the expression for “varepsilon” and “varphi = 600rad” and expressing “omega_0”, obtain:
“omega_0 = dfrac{varphi}{Delta t}-dfrac{Delta omega }{2}\nomega_0 = dfrac{600rad}{7s}-dfrac{100rad/s}{2} approx 35.7space rad/s”
Answer. 1) 35.7 rad/s, 2) 14.3 rad/s^2.
