To understand and apply the formula = I to rigid objects rotating about a fixed

Question

To understand and apply the formula =I to rigid objects rotating about a fixed axis.

To find the acceleration a of a particle of mass m, we use Newton's second law: F net=ma , where F net is the net force acting on the particle.

To find the angular acceleration of a rigid object rotating about a fixed axis, we can use a similar formula: net=I, where net= is the net torque acting on the object and I is its moment of inertia.

In this problem, you will practice applying this formula to several situations involving angular acceleration. In all of these situations, two objects of masses m1 and m2 are attached to a seesaw. The seesaw is made of a bar that has length l and is pivoted so that it is free to rotate in the vertical plane without friction.Assume that the pivot is attached tot he center of the bar.

You are to find the angular acceleration of the seesaw when it is set in motion from the horizontal position. In all cases, assume that m1>m2.

Assume that the mass of the swing bar, as shown in the figure, is negligible.(Figure 1) Find the magnitude of the angular acceleration of the seesaw.

Express your answer in terms of some or all of the quantities m1, m2, l, as well as the acceleration due to gravity g.

Explanation / Answer

= T/I, where T = torque and I = moment of inertia

Therefore,

T = m1*g*L/2 - m2*g*L/2

= L/2*9*(m1 - m2)
I = m1*(L/2)² + m2*(L/2)²

= (m1 + m2)*(L/2)²

= L/2*g*(m1 - m2)/[L/2*(m1+ m2)*(L/2)²]

= 2*[(m1 - m2)/(m1 + m2)]*g/L

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.