Physics : A discus thrower accelerates a discus from rest

Subject: Physics / General Physics
Question
1) A discus thrower accelerates a discus from rest to a speed of 24.9 m/s by whirling it through 1.22 rev. Assume the discus moves on the arc of a circle 1.01 m in radius.

(a) Calculate the final angular speed of the discus.
————— rad/s

(b) Determine the magnitude of the angular acceleration of the discus, assuming it to be constant.
—————— rad/s2

(c) Calculate the time interval required for the discus to accelerate from rest to 24.9 m/s.
——————– s

2) A car accelerates uniformly from rest and reaches a speed of 21.9 m/s in 8.92 s. Assume the diameter of a tire is 58.3 cm.

(a) Find the number of revolutions the tire makes during this motion, assuming that no slipping occurs.
——————– rev

(b) What is the final angular speed of a tire in revolutions per second?

—————- rev/s

3) Find the net torque on the wheel in the figure below about the axle through O, taking a = 7.00 cm and b = 25.0 cm. (Assume that the positive direction is counterclockwise.)
———- N · m

4) The combination of an applied force and a friction force produces a constant total torque of 35.4 N · m on a wheel rotating about a fixed axis. The applied force acts for 5.90 s. During this time, the angular speed of the wheel increases from 0 to 10.1 rad/s. The applied force is then removed, and the wheel comes to rest in 60.1 s.

(a) Find the moment of inertia of the wheel.
————– kg · m2

(b) Find the magnitude of the torque due to friction.
————— N · m

(c) Find the total number of revolutions of the wheel during the entire interval of 66.0 s.

—————- revolutions.

5) The four particles shown below are connected by rigid rods of negligible mass where y1 = 6.50 m. The origin is at the center of the rectangle. The system rotates in the xy plane about the z axis with an angular speed of 5.90 rad/s.

(a) Calculate the moment of inertia of the system about the z axis.
—————— kg · m2

(b) Calculate the rotational kinetic energy of the system.
—————— J

6) A thin, cylindrical rod ? = 27.8 cm long with a mass m = 1.20 kg has a ball of diameter d = 10.00 cm and mass M = 2.00 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top as shown in the figure below. The combination is free to pivot about the bottom end of the rod after being given a slight nudge.

(a) After the combination rotates through 90 degrees, what is its rotational kinetic energy?
———————— J

(b) What is the angular speed of the rod and ball?
————— rad/s

(c) What is the linear speed of the center of mass of the ball?
————— m/s

(d) How does it compare with the speed had the ball fallen freely through the same distance of 32.8 cm?

vswing is Select—– greater than less than vfall by ————– %.

7) A uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height h.

(a) If they are released from rest and roll without slipping, which object reaches the bottom first?

Solid

diskuniform hoop

it’s a tie
(b) Verify your answer by calculating their speeds when they reach the bottom in terms of h. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)

vdisk

=

vhoop

=

8) A cylinder of mass 6.0 kg rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speed of 15.0 m/s.

(a) Determine the translational kinetic energy of its center of mass.
—————- J

(b) Determine the rotational kinetic energy about its center of mass.

————— J

(c) Determine its total energy.

————— J

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