A 1.62 oz golf ball with a 1.70 in. diameter is hit by a club at point P. Velocitymagnitude of the ball's center of mass is 180 ft/s after the impact. What is the angular velocity of the ball? (h = 0.2 in.)

A 1 oz. bullet with a horizontal velocity of 350 ft/s strikes a circular disk. The bullet is embedded into the disk after impact. What is the angular velocity of the cylinder with the embedded bullet after impact? The disk weighs 8 lb and has a radius of 1.2 ft. Assume the bullet's mass is uniformly distributed in the disk after impact.

Please see the attachment and ignore the 3rd problem.

A 4 kg uniform rod is at rest on the frictionless horizontal x-y plane when it is struck by a 1 kg disk as shown. The coefficient of restitution of the collision is 0.6. What is the angular velocity of the rod after collision? Neglect the friction between the disk and the rod.

A bullet weighing 2 oz was fired horizontally into a 100 lb sand box suspended on a rope 3 ft long as shown. It was calculated from the observed angle that the box with the bullet embedded in it swung to a height of 0.097 ft. What was the speed of the bullet as it entered the box? Assume the box is small and acts like a particle.

A.) Mass of the ball, m = 1.62 oz = 1.62/16 lb
radius of the ball, r = 1.7/2 in = 1.7/(2*12) ft
h = 0.2 in = 0.2/12 ft
speed of the ball after the impact, v = 180 ft/s

moment of inertia of the ball, I = (2/5)*m*r^2
Let us assume the impulse be Im, and angular velocity of the ball be, w.

Hence, by linear momentum, Im = m*v

By angular momentum
Im*h = I*w
=> w = Im/w = m*v*h/(2*m*r^2/5)
=> w = 5*v*h/(2*r^2) = 5*180*(0.2/12)/(2*(1.7/(2*12))^2)
=> w = 1494.8 rad/s ~= 1490 rad/s --Answer(b)

1.) mass of the bullet mb = 1 oz = 1/16 lb
speed of the bullet before collision vb = 350 ft/s
radius of the disk R = 1.2 ft
mass of the disk md = 8 lb

moment of inertia of the disk about O, Id = (1/2)md*R^2 + md*R^2 = (3/2)*md*R^2 = 1.5*8*1.2^2 = 1
7.28 lb.ft^2
After impact moment of inertia of the bullet about O, Ib = ...

Solution Summary

This solution is provided in approximately 788 words. It uses linear momentum and angular momentum law to calculate angular velocity and uses energy law to calculate displacement.

The rigid body shown in this diagram is moving such that the velocities of points A and B are the same. The magnitude of the velocity of point A is 25m/s and the distance between points A and B is 10m.
Determine the magnitude of the angularvelocity of the rigid body.
Express your answer in rad/s and give you answer to 4

Question: The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angular acceleration as the blades slow down? The initial rotation is in the positive direction.

Please see attached.
1. The two spheres of equal mass m are able to slide along the rotating horizontal black rod. If they are initially latched in position a distance r from the axis of rotation with the assembly rotating freely with an angularvelocity of Wo.
Determine the new angularvelocity Wf after the spheres are rele

A 1.10 m-long massless rod is pivoted at one end and swings around in a circle on a frictionless table. A block with a hole through the center can slide in and out along the rod. Initially, a small piece of wax holds the block 10.0 cm from the pivot. The block is spun at 50.0 rpm, then the temperature of the rod is slowly increa

Q: "The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angular acceleration as the blades slow down? The initial rotation is in the positive direction."
The OTA's solution is attached. We both got an answer of 208 rad/s^2.

A large turntable rotates about a fixed vertical axis, making one revolution in a time of T. The moment of inertia of the turntable about this axis is I. A child with a mass of m, initially standing at the center of the turntable, runs out along a radius.
What is the angular speed of the turntable when the child is a distance

The 6lb slender rod AB is originally shown at rest, suspended in the vertical position. A 1lb ball is thrown at the rod with the velocity v= 50ft/s and strikes the rod at C. Determine the angularvelocity of the rod just after the impact. Take e = 0.7 and d= 2ft. (See attachment for diagram)

a) A body of mass m kg is attached to a point by string of length 1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the point of attachment, calculate its angularvelocity.
b) If the mass rotates on a table, calculate the force on the table when the speed of rotation is 25 rpm and the mass is 6 kg.

See attachment please.
Need FBD for each case.
The 0.2 kg ball ( ball is sliding not rotating) and the supporting cord are revolving about the vertical axis on the fixed smooth conical surface with an angularvelocity of W = 4 radians/sec. The green ball is held in position b = .3 m by the tension T in the yellow cord.
If b

A pitcher throws a curveball that reaches the catcher in 0.53 s. The ball curves because it is spinning at an average angularvelocity of 335 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher?