85. A uniform cylinder of mass M and radius R is initially at rest on a rough horizontal surface. A light string is wrapped around the cylinder and is pulled straight up with a force T whose magnitude is 0.80 Mg. As a resuit, the cylinder slips and accelerates horizontally. The moment of inertia of the cylinder is I =MR2 and the coefficient of kinetic friction is 0.40. a 5:l0.4)Mg On the circle above, show all the forces applied on the cylinder. b. In terms of g, determine the linear acceleration, a of the center of the cylinder. Determine the angular acceleration, a of the cylinder. d. Explain the difference in results of linear acceleration a, and Ra. a. C. velocity elocity a

A proton is accelerated in a cyclotron to 5.0106m/s in 0.01 s. The proton follows a circular path. If the radius of the cyclotron is 0.5 km, (a) What is the angular momentum of the proton about the center at its maximum speed? (b) What is the torque on the proton about the center as it accelerates to maximum speed?

A particle has mass 0.5 kg and is traveling along the line x=5.0m at 2.0 m/s In the positive y-direction. What is the particle’s angular momentum about the origin?

1. 5r2 and I have two disks. I know that disk A has a mass per unit area o given by o = disk B has o = 3r3. Each disk has radius 10cm. I have a slope at angle 45 degrees to the horizontal that is 2 m long. I time with a stop watch how long it takes the disks to roll down the slope without slipping. (Assuming that the disk's are let go with zero velocity at the top of the slope). a) Calculate the mass of each disk. [4 marks]

Three dimensions. Three point particles are fixed in place in an xyz coordinate system. Particle A, at the origin, has mass ma. Particle B, at xyz coordinates (3.00d, 1.00d, 3.00d), has mass 4.00ma, and particle C, at coordinates (-2.00d, 1.00d, -1.00d), has mass 2.00ma. A fourth particle D, with mass 3.00ma, is to be placed near the other particles. If distance d = 4.50 m, at what (a) x, (b) y, and (c) z coordinate should D be placed so that the net gravitational force on A from B, C, and D is zero? (a) Number Units (b) Number |Units (c) Number Units

A Lazy Susan (M=0.5 kg) in the shape of a disk is free to rotate about its center withoutfriction. It is initially motionless when a Texas-sized cockroach (m=10 g) starts runningCCW along the rim. The angular speed of the Lazy Susan is then 1 rad/sec. With whatspeed is the cockroach running (in the rest frame of the table, not the Lazy Susan)? We symbolically solve the problem without the value of R

A disc, with a non-zero initial angular velocity, undergoes a constant angular acceleration for T seconds ( i.e., 3.1415... seconds). In that time it rotates through two complete revolutions and has a final angular velocity of 3.5 radians/sec. What is its initial angular velocity in radians/second?

Two identical spheres with m 3 kg each are rigidly attached to the rotating light rigid structure. The velocity of the spheres is v = 2 m/s. Determine the angular momentum about the axis of rotation. 5 13 0.3 m 0.2 m m' H, = 7.20 kg · O H, 1.80 kg· m2 %3D O H. 3.60 kg. m' H. = 6.00 kg .

Two equal 16.5 kg masses are at the ends of a 4.6 kg 60.5 cm rod that is initially spinning about the rods center at 55.7 rev./sec. suddenly the rods length is increased to 92.3 cm. How fast is the rod (& masses) spinning now? Neglect any frictional interactions in the axle. Enter in your in rev./sec.

Jeremy is playıng WHh avoyo 07 mass mo=Daa grams. The yoyo String is iet out to hoizontalCiYcie at a cotant rate 07 Wo=5.10 rads sec. The YoyO o rs=58 am,and he spins the yoy0 in a length String makes an ang le 07 Os With the horizontal1 angle Os indegres - calculate the Hena nonetons