Two mass particles, m_1 = 0.1 kg and m_2 = 0.2 kg are attached to a rotating boa

Question

Two mass particles, m_1 = 0.1 kg and m_2 = 0.2 kg are attached to a rotating board at radius r_1 = 50cm and r_2 = 100 cm from origin. The initial position and final position Determine and compare the followings: a) Their angular velocities and [linear] velocities, b) angular momentum, c) centripetal force and d) kinetic energy. [Only one of them will be graded] Assuming the angular speed is constant, what is the period of the angular motion of the particles? Rotation kinematics equations. (One of them is missing, what is that?) theta = theta_0 + omega t theta = theta_o + omega_o t + 1/2 alpha t^2 omega = omega_o + alpha t alpha = const or average omega^2 = omega_0^2 + 2 alpha Delta theta If it takes a hard drive to speed up from 0 to 7200 rpm in just 10.0 ms (ms = milliseconds), how would you answer the following questions a) What is the total distance angular displacement? b) What is the [linear] speed of the mass particle located at 5 cm from center at the disc. (Only one of these above will be graded] and tangential acceleration?

Explanation / Answer

1) a) w1 = 0.72pi/2.5 = 0.907 rad/s = w2

b) v1 = r1w1 = 0.5*0.907 = 0.453 m/s

v2 = r2w2 = 0.907 m/s

v2>v1

c) angular momentum = m1v1r1 = 0.0226 kg m/s

L2 = m2v2r2 = 0.181 kg m/s

L2>l1

d) f1 = mv1^2/r1 = 0.041 N

f2 = m2v2^2/r2 = 0.164 N

f2>f1

e) k1 = 1/2m1v1^2 = 0.01 J

k2 = 0.082 J

k2>k1

2) w = change in angular displacement/time

time =  change in angular displacement/w

3) first equation is not kinematic equation

4) theta = 7200*2*3.14/60*10*10^-3 = 7.54 rad

b) v = rw = 0.05*7200*2*31.4/60 = 37.68 m/s

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