Worksheet 5 (PH 105-004, Roshan Koirala) Name:haotpbe auno Question1 A solid sph

Question

Worksheet 5 (PH 105-004, Roshan Koirala) Name:haotpbe auno Question1 A solid sphere of radius 24 cm is positioned at the top of an incline that makes 26° angle with the horizontal. This initial position of the sphere is a vertical distance 3.4 m above its position when at the bottom of the incline. The sphere is released and moves down the incline. Find the speed of the sphere when it reaches the bottom of the incline if it rolls without slipping. ,2ys 24 em Question 2 A string is wound around a uniform disc of radius 0.62 m and mass 3.4 kg. The disc is released from rest with the string vertical and its top end tied to a fixed support. The acceleration of gravity is 9.8 m/s. As the dise descends, calculate the tension in the string. 0.62 m 2.9(4.8- 3.4 kg 3 Question 3 A student sits on a rotating stool holding two 3.8 kg masses. When his arms are extended horizontally, the masses are 0.88 m from the axis of rotation, and he rotates with an angular velocity of 2 rad/sec. The student then pulls the weights horizontally to a shorter distance 0.22 m from the rotation axis and his angular velocity increases to o2. For simplicity, assume the student himself plus the stool he sits on have constant combined moment of inertia I, 4.6 kg m. Find the new angular velocity ø2 of the student after he has pulled in the weights.

Explanation / Answer

3.

Using angular momentum conservation:

Li = Lf

I1*w1 = I2*w2

I1 = Is + 2*m*r1^2

I1 = 4.6 + 2*3.8*0.88^2 = 10.48 kg-m^2

If = Is + 2*m*r2^2 = 4.6 + 2*3.8*0.22^2 = 4.98 kg-m^2

w1 = 2 rad/sec

w2 = ?

w2 = I1*w1/I2

Using known values:

w2 = 10.48*2/4.98

w2 = 4.21 rad/sec

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