(a) (b) (c) (d)

A figure skater is spinning with an angular velocity of +16.4 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +3.65 rad. Determine (a) her average angular acceleration and (b) the time during which she comes to rest.

At the moment of take-off, a diver's moment of inertia (I) was 50 kgm^2 and angular velocity about a mediolateral axis was 90 degrees/s. later in the dive, I (moment of inertia) changed to 15 kgm^2. What was the new angular velocity?

Consider the image below of a hammer throw. At the point of release of the hammer, an athlete has an angular velocity of 2.70 rad/sec. If we assume that the length of the athlete’s arms plus the hammer is 1.5 m, and that the angular acceleration of the athlete and hammer at this instant is 0.65rad/sec2, what is the a) tangential velocity, the b) tangential acceleration, and the c) centripetal acceleration of the hammer mass?

You are riding your bicycle down the road and decide to stop to take in the scenery. Initially, your bicycle tires are rotating at a frequency of 7 times per second. If it takes your bicycle 50 revolutions to come to a full stop, what is the magnitude of the angular acceleration (assume your acceleration is constant). Give your answer in units of radians per second squared

A ceiling fan can accelerate from rest to 2pi rad/s in 8 seconds. (A) what is the angular acceleration of the fan? (B) find the angular displacement of the fan during the first 5 seconds. (C) at the full angular speed of 2pi rad/s find the corresponding tangential speed of a point at the rim of the wing if the radius of the wing is r=0.5m. (D) what is the centripetal acceleration of a point at the rim (r=0.5 m) when the fan reaches full speed? can you give detailed steps please?

1. The horizontal circular platform weighs 500 lb and has a radius of gyration of kz = 8 ft from the z-axis passing through O. The platform is free to rotate about the z-axis and is initially at rest. A person having a weight of 150 lb begins to run along the edge in a circular path of radius 10 ft. If they maintain a speed of 4 ft/s relative to the platform, determine the angular velocity of the 10 ft platform. Neglect friction. I don't think we have dealt with relative velocity in this context, but it follows our earlier relative velocity treatment. Here all speeds are in the t-direction. vp is the speed of the person, and vp is the speed of the disk at the location of the person. Then vp = vp + Vp/D, same as before. You are given vpp = 4 ft/s.