Question

A 5.0 kg rod with a length of 2.8 m has an axis of rotation at its center. Looking at the rod with its axis perpendicular to this page, a force of 14.5 N at 68^o is applied to the rod 1.1 m from the axis of rotation. This torque would angularly accelerate the rod in a counter-clockwise direction. Assume that the torque continues to be applied during the motion consider in this problem and that there are no other torques. Consider the counter-clockwise direction to be positive. At t_o = 0.00 s, the angular velocity of the rod is 3.6 rad/s. Avoid round-off error in the later answers. Unless directed otherwise, keep four significant digits.

Calculate Rotational Inertia and net torque that acts upon the rod.

What is the angular acceleration? Calculate your answer using the four-digit results from the questions above.

What is ω_o equal to in this problem? Input only two digits.

Calculate ω, when t = 5.6 s. Use the four-digit result for angular acceleration when calculating, but input the answer with only two significant digits.

What is Δθ, when t = 7.9 s? Use the four-digit result for angular acceleration when calculating, but input the answer with only two significant digits using scientific “E” notation. For example, 560 would be entered as 5.6E2.   

Answer 1

(a) Given mass of the rod M =5kg, length of the rod L = 2.8m. It is rotating about its centre about an axis perpendicular to the page. The rotational inertia of the rod about this axis is given by

So the rotational inertia of the upto four significant figures is 3.267kgm2.

The force applied is F = 14.5N is applied at a distanceR = 1.1m from the axis of rotation at an angle = 68. This force has a sin component and cos component. But only sin component can rotate the rod. Therefore the torque acting on the rod is

So the net torue acting on the rod upto four significant figures is 14.79Nm.

(b) If I is the moment of inertia and is the angular acceleration, then the torque acting on the rod is given by

So the angular acceleration of the rod upto four significant figures is 4.527rad/s2.

(c) At t = 0.00s the angular velocity of the rod is 3.6rad/s. So the initial angular velocity = 3.6rad/s.

(d) At t = 5.6s, the angular velocity is . Its is given by

So the angular velocity of the rod at t=5.6s upto two significant figures is 25 rad/s.

(e) At t = 0, the initial angular displacement =0. At t = 7.9s, the angular displacent is given by

So the change in angular displacement is

So the change in angular displacemet of the rod at t=7.9s upto two significant figures using scientific notation E is 25 1.4E2 rad.