23% 11: 09 AMLTE1. Initially, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocityof 3.0 rad/sec. Two seconds later it has turned through 5.0 complete revolutions. Find the angularacceleration2. Given the position vector r= 3i + 4j +5k and force F = 16i - 20j - 5 k, find the magnitude of thetorque vectort so that t = r x F ? (Hint: use 3x3 matrix)A solid disk of mass equal to 7.0 kg and radius of 30 cm changes its rotations gradually from 45 rpm to120 rpm in 5.0 sec3. find the angular acceleration in rad/s.4. how many revolutions has the disk turned in this 5.0 seconds?5. find the change in rotational kinetic energy6. find its moment of inertia in kgm27. find the magnitude of torque needed to make such a change in rpm.8. find the tangential acceleration of a point P on the outer rim of the disk.20t2The fan blade in a jet engine rotates from rest with the angular acceleration a =9. find the angular velocity as a function of time.10. find the angular displacement as a function of time.11. if the rotational inertia of the blade is 5.0 kgm2, find the work done on the blade in the first initial3.0 seconds. (Hint: take t from zero to 3 and d0 = odt)A hollow sphere ( M = 3.0 kg and R = 60 cm ) is rolling down an inclined surface with a height of 2.0meters and an inclined angle of 25 degrees.12. find the moment of inertia of the sphere, in kgm213. find the speed of the center of mass when it reaches the bottom of the hill14. find the total rotational kinetic energy at the bottomhך

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Asked Nov 21, 2019
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Part 9 10 11

23% 11: 09 AM
LTE
1. Initially, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity
of 3.0 rad/sec. Two seconds later it has turned through 5.0 complete revolutions. Find the angular
acceleration
2. Given the position vector r= 3i + 4j +5k and force F = 16i - 20j - 5 k, find the magnitude of the
torque vectort so that t = r x F ? (Hint: use 3x3 matrix)
A solid disk of mass equal to 7.0 kg and radius of 30 cm changes its rotations gradually from 45 rpm to
120 rpm in 5.0 sec
3. find the angular acceleration in rad/s.
4. how many revolutions has the disk turned in this 5.0 seconds?
5. find the change in rotational kinetic energy
6. find its moment of inertia in kgm2
7. find the magnitude of torque needed to make such a change in rpm.
8. find the tangential acceleration of a point P on the outer rim of the disk.
20t2
The fan blade in a jet engine rotates from rest with the angular acceleration a =
9. find the angular velocity as a function of time.
10. find the angular displacement as a function of time.
11. if the rotational inertia of the blade is 5.0 kgm2, find the work done on the blade in the first initial
3.0 seconds. (Hint: take t from zero to 3 and d0 = odt)
A hollow sphere ( M = 3.0 kg and R = 60 cm ) is rolling down an inclined surface with a height of 2.0
meters and an inclined angle of 25 degrees.
12. find the moment of inertia of the sphere, in kgm2
13. find the speed of the center of mass when it reaches the bottom of the hill
14. find the total rotational kinetic energy at the bottom
h
ך
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23% 11: 09 AM LTE 1. Initially, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 3.0 rad/sec. Two seconds later it has turned through 5.0 complete revolutions. Find the angular acceleration 2. Given the position vector r= 3i + 4j +5k and force F = 16i - 20j - 5 k, find the magnitude of the torque vectort so that t = r x F ? (Hint: use 3x3 matrix) A solid disk of mass equal to 7.0 kg and radius of 30 cm changes its rotations gradually from 45 rpm to 120 rpm in 5.0 sec 3. find the angular acceleration in rad/s. 4. how many revolutions has the disk turned in this 5.0 seconds? 5. find the change in rotational kinetic energy 6. find its moment of inertia in kgm2 7. find the magnitude of torque needed to make such a change in rpm. 8. find the tangential acceleration of a point P on the outer rim of the disk. 20t2 The fan blade in a jet engine rotates from rest with the angular acceleration a = 9. find the angular velocity as a function of time. 10. find the angular displacement as a function of time. 11. if the rotational inertia of the blade is 5.0 kgm2, find the work done on the blade in the first initial 3.0 seconds. (Hint: take t from zero to 3 and d0 = odt) A hollow sphere ( M = 3.0 kg and R = 60 cm ) is rolling down an inclined surface with a height of 2.0 meters and an inclined angle of 25 degrees. 12. find the moment of inertia of the sphere, in kgm2 13. find the speed of the center of mass when it reaches the bottom of the hill 14. find the total rotational kinetic energy at the bottom h ך

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Expert Answer

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9), Angular acceleration is the rate of change of angular velocity. The equation for the angula acceleration is given by do dt Here, is the angular velocity Rearranging the above equation, do adt 20t2dt Integrating both sides, 9=f20r°dt 20t3 +C 3 Since the starts from rest its angular velocity at t = 0 will be zero. Applying this condition, 20 (0) +C 3 C 0

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Thus 20t3 0 3 2023 3 10), Angular velocity is the rate of change of angular displacement. It is given by de dt Rearranging the above equation, de= adt 20t3 -dt = Integrating both sides 20r3 e= -dt 3 20 t +C 3 4 3

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Angular displacement will be zero at t = 0. Applying the initial condition, 0 0 C C 0 Thus, 5 e=-t* + 0 4. 0 = _t 3 The work done will be equal to its change in rotational kinetic energy. This can be given as, W = [rd0 Here, W is the work done and r is the torque The torque is, 1(20r2) = 201t2 And de adt 203 -dt 3

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