Help me study for my Physics class. I’m stuck and don’t understand.

1. The angular position of a point on a rotating wheel is given by θ = 7.76 + 8.36t2 + 1.80t3, where θ is in radians and t is in seconds. At t = 0, what are (a) the point’s angular position and (b) its angular velocity? (c) What is its angular velocity at t = 4.82 s? (d) Calculate its angular acceleration at t = 2.46 s. (e) Is its angular acceleration constant?

2. A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at

6.30 rev/s
; 40.0 revolutions later, its angular speed is

22.0 rev/s
. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 40.0 revolutions, (c) the time required to reach the

6.30 rev/s
angular speed, and (d) the number of revolutions from rest until the time the disk reaches the

6.30 rev/s
angular speed.

3. A flywheel with a diameter of 2.42 m is rotating at an angular speed of 114 rev/min. (a) What is the angular speed of the flywheel in radians per second? (b) What is the linear speed of a point on the rim of the flywheel? (c) What constant angular acceleration (in revolutions per minute-squared) will increase the wheel’s angular speed to 1170 rev/min in 123 s? (d) How many revolutions does the wheel make during that 123 s?

4. A gyroscope flywheel of radius

2.59 cm
is accelerated from rest at

19.0 rad/s2
until its angular speed is

2690 rev/min
. (a) What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process? (b) What is the radial acceleration of this point when the flywheel is spinning at full speed? (c) Through what distance does a point on the rim move during the spin-up?

5. The figure gives angular speed versus time for a thin rod that rotates around one end. (a) What is the magnitude of the rod’s angular acceleration? (b) At t = 4.0 s, the rod has a rotational kinetic energy of 1.92 J. What is its kinetic energy at t = 0?

6. Some European trucks run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of 130 π rad/s. One such flywheel is a solid, uniform cylinder with a mass of 470 kg and a radius of 0.763 m. (a) What is the kinetic energy of the flywheel after charging? (b) If the truck uses an average power of 6.1 kW, for how many minutes can it operate between chargings?

 

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