There are particles 1 and 2, each of mass m, attached to the ends of a rigid massless rod of length..?

Question

L1 +L2, with L1 = 20cm and L2 = 80cm. The rod is held horixontally on the fulcrum and then released. What are the magintudes of the initial acceleratoins of (a) particle 1 and (b) particle 2?

Answer 1

The equation involved is
T = I * alpha where T = Torque; I = moment of inertia and alpha = angular acceleration.
For this system,
I = m*L1^2 + m*L2^2
= m*(20^2 + 80^2) * 10^-4 kgm^2
Initial torque T = m * g * (80-20) *10^-2 J
this gives alpha = T / I = 8.65 rad/s^2.
Linear acceleration = r * alpha
Hence a1 = 8.65 * 0.2 = 1.73 m/s^2
a2 = 8.65 * 0.8 = 6.92 m/s^2

Answer 2

properly you detect the complete torque of the equipment. i will substitute mass m to M for readability. Now bear in techniques torque is T=F(x)r the place x is the crossproduct, or to that end multiplication through fact the rods are perpendicular to the acceleration, yet for added clarification you are able to reference my source. F is the rigidity and r is the radius. And F = M*a the place a is acceleration. in case you integrate the formulation you get T = M*a*r subsequently particle a million will grant a counter clockwise torque of M*1m*g, the place g is acceleration through gravity. particle 2 will grant a clockwise torque of M*5m*g. the complete torque then is M*5m*g - M*1m*g = M*4m*g CLOCKWISE. the complete torque would be an identical through fact the torque on each and each individual particle, so which you will say M*4m*g = M * a * r for each particle, the place r and a are distinctive for each particle. For particle a million the radius is 1m, and for particle 2 the radius is 5m. The Ms cancel giving you 4m*g/r=a particle a million would have acceleration of (4/a million)*g, and particle 2 would have an acceleration of (4/5)*g Now, pay interest to the path: We reported it replaced into going CLOCKWISE, precise? meaning that particle a million would be going UP (ie constructive acceleration), whilst particle 2 would be occurring (ie adverse acceleration) and that's it. Cheers