A puck goes around its circular path once every 1.17 s. Its speed is 97.5 cm/s.

Question

                A puck goes around its circular path once every 1.17 s. Its speed is 97.5 cm/s. The radius of its circular path is      cm.?

                A 1.05 kg mass moves in a circle of radius 0.855 m at a speed of 5.30 m/s. The centripetal force is      Newtons.

                If you choose a scale of 1.0 cm = 1.9 cm/s, you would represent a velocity of 46.0 cm/s as a vector      cm long.

A 12.0 kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 9.0 m/s.

A student sits on a rotating stool holding two 2.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg

Explanation / Answer

1)
v = 2*pi*r/t

r = v*t/(2*pi) = 0.1816 m = 18.16 cm

2) F = m*v^2/r = 34.5 N

3) 46/1.9 = 24.21 cm

4)

a)KE1 = 0.5*m*v^2 = 486 J

b) KE2 = 0.5*I*w^2
her I = (0.5)*m*r^2


KE = 0.5*0.5*m*r^2*w^2

and v = r*w

KE = 0.25*m*v^2 = 243 J

c) KE = KE1 + KE2 = 729 J



5)
a)I1 = 3 + 2*2*1^2 = 7 kg.m^2

I2 = 3+ 2*2*0.5^2 = 4 kg.m^2

L1 = L2

I1*w1 = I2*w2
W2 = (I1/I2)*w1 = (7/4)*0.75 = 1.3125 rad/s

b)

before = 0.5*I1*w1^2 = 1.96875 J

after = 0.5*I2*w2^2 = 3.4453125 J

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