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Nanabit

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1. A bowling ball has a mass of 5.00 kg, a moment of inertia of 1.60 10-2 kg · m2, and a radius of 0.100 m. If it rolls down the lane without slipping at a linear speed of 5.00 m/s, what is its total energy?

I figured, through adding rotational KE for a sphere to the normal formula for KE, that the total KE formula would be (7/10)mv^2. I got 87.5 J, which isn't right. Should I not be using this formula?

2. A ring of mass 2.53 kg, inner radius 6.00 cm, and outer radius 8.00 cm is rolling (without slipping) up an incline plane which makes an angle of = 36.4°. At the moment the ring is at position x = 2.00 m up the plane, its speed is 2.75 m/s. The ring continues up the plane for some additional distance, and then rolls back down. It does not roll off the top end. How far up the plane does it go?

I can figure out the moment of inertia for the ring, no problem. I got .01265 kgm^2 for that. Then I thought I could figure out the final velocity by using conservation of momentum. (2.53kg)(9.80m/s^2)(2.00m))+(1/2)(2.53kg)(2.75 m/s)^2 = (1/2)(2.53kg)(vf^2). I got the final velocity to be 5.55 m/s. I don't know where to go from there. I thought if I could find acceleration I could use kinematics to figure out the final x distance, but I don't know how to find acceleration.

3. A force of F = 3.00 i + 2.00 j N is applied to an object that is pivoted about a fixed axis aligned along the z coordinate axis.

(a) If the force is applied at the point r = (4.00 i + 7.00 j + 0 k) m, find the magnitude of the net torque about the z axis. N · m

(b) What is the direction of the torque vector?

I have no problem with part a, I found that to be 13Nm. I just don't know how to tell the direction of the torque vector.

4. A uniform solid disk of mass 2.98 kg and radius 0.200 m rotates about a fixed axis perpendicular to its face.

(a) If the angular speed is 5.95 rad/s, calculate the angular momentum of the disk when the axis of rotation passes through its center of mass.

(b) What is the angular momentum when the axis of rotation passes through a point midway between the center and the rim?

Once again, no problem with part a. Part b I thought I could just divide the radius by 2 and multiply that by the angular speed, but it isn't right.

5. The hour and minute hands of Big Ben, the famous Parliament Building tower clock in London, are 2.60 m and 4.60 m long and have masses of 59.0 kg and 99 kg, respectively. Calculate the total angular momentum of these hands about the center point. Treat the hands as long thin rods.

I'm lost.

6. A playground merry-go-round of radius R = 1.60 m has a moment of inertia I = 235 kg · m2 and is rotating at 12.0 rev/min about a frictionless vertical axle. Facing the axle, a 24.0 kg child hops onto the merry-go-round and manages to sit down on its edge. What is the new angular speed of the merry-go-round?

This one makes perfect sense to me, but it's not working out. I figured first I had to figure out the initial mass. I = (1/2)mr^2. 235 kg = m (1.60m)^2. mass = 183.6 kg. Then add for the final moment of inertia the weight of the child. I = (1/2)mr^2. I = (1/2)(207.6kg)(1.60m)^2. I = 265.7Kgm^2. Then use the formula Iiwi = Ifwf. (235kgm^2)(1.26rad/sec)=(265.7kgm^2)(wf). I got 1.11 rad/sec to be the answer, but the answer has to be in rev/min, so I got 10.6 rev/min and have no idea why it is wrong.

7. A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P11.51. The sphere starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, which is much larger than r. a) What is the minimum value that h can have if the sphere is to complete the loop? (Use R for R, m for m, r for r, and g for gravity, as necessary.)

(b) What are the force components on the sphere at the point P if h = 3R?

Fx = N

Fy = N

I'm lost.

Thanks again for any help.