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(Figure 1) shows a slender uniform rod with mass M and length L. It might be a baton held by a twirler in a marching band (without the rubber end caps). (a) Use integration to compute its moment of inertia about an axis through O, at an arbitrary distance from one end. (b) Initially the rod is at rest. It is given a constant angular acceleration of magnitude a around the axis through O. Find how much work is done on the rod in a time t. (c) At time t, what is the linear acceleration of the point on the rod farthest from the axis? Completed EVALUATE Part H Use your expression of the moment of inertia for the special cases A=0 (the axis passes through one end of the rod) and h = 1/2 (the axis passes through the middle of the rod). Express your answers in terms of M and I separated by a comma. ΘΕΙ ΑΣΦ I=0, In-/= ?

(Figure 1) shows a slender uniform rod with mass M and length L. It might be a baton held by a twirler in a marching band (without the rubber end caps). (a) Use integration to compute its moment of inertia about an axis through O, at an arbitrary distance from one end. (b) Initially the rod is at rest. It is given a constant angular acceleration of magnitude a around the axis through O. Find how much work is done on the rod in a time t. (c) At time t, what is the linear acceleration of the point on the rod farthest from the axis? Completed EVALUATE Part H Use your expression of the moment of inertia for the special cases A=0 (the axis passes through one end of the rod) and h = 1/2 (the axis passes through the middle of the rod). Express your answers in terms of M and I separated by a comma. ΘΕΙ ΑΣΦ I=0, In-/= ?

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(Figure 1) shows a slender uniform rod with mass M and length L. It might be a baton held by a twirler in a marching band (without the rubber end caps). (a) Use integration to compute its moment of inertia about an axis through O, at an arbitrary distance from one end. (b) Initially the rod is at rest. It is given a constant angular acceleration of magnitude a around the axis through O. Find how much work is done on the rod in a time t. (c) At time t, what is the linear acceleration of the point on the rod farthest from the axis? Figure M- 1 of 1 Mass element: rod segment of length dr Completed EVALUATE Part H Use your expression of the moment of inertia for the special cases h = 0 (the axis passes through one end of the rod) and h= 1/2 (the axis passes through the middle of the rod). Express your answers in terms of M and I separated by a comma I-0, In-Li2= Submit Part I ΕΘΕΙ ΑΣΦΑ Request Answer A C ? Is the acceleration magnitude from Part G constant? Would you expect it to be? Submit Request Answer Yes, because the angular acceleration is constant. O No, because the tangential component of the acceleration depends on time. O No, because the radial component of the acceleration depends on time. Part H Use your expression of the moment of inertia for the special cases h=0 (the axis passes through one end of the rod) and h=L//2 (the axis passes through the middle of the rod). Express your answers in terms of M and L separated by a comma. I_(h=0),I_(h=L//2)= Part I Is the acceleration magnitude from Part G constant? Would you expect it to be? Yes, because the angular acceleration is constant. No, because the tangential component of the acceleration depends on time. No, because the radial component of the acceleration depends on time.
Transcribed Image Text:(Figure 1) shows a slender uniform rod with mass M and length L. It might be a baton held by a twirler in a marching band (without the rubber end caps). (a) Use integration to compute its moment of inertia about an axis through O, at an arbitrary distance from one end. (b) Initially the rod is at rest. It is given a constant angular acceleration of magnitude a around the axis through O. Find how much work is done on the rod in a time t. (c) At time t, what is the linear acceleration of the point on the rod farthest from the axis? Figure M- 1 of 1 Mass element: rod segment of length dr Completed EVALUATE Part H Use your expression of the moment of inertia for the special cases h = 0 (the axis passes through one end of the rod) and h= 1/2 (the axis passes through the middle of the rod). Express your answers in terms of M and I separated by a comma I-0, In-Li2= Submit Part I ΕΘΕΙ ΑΣΦΑ Request Answer A C ? Is the acceleration magnitude from Part G constant? Would you expect it to be? Submit Request Answer Yes, because the angular acceleration is constant. O No, because the tangential component of the acceleration depends on time. O No, because the radial component of the acceleration depends on time. Part H Use your expression of the moment of inertia for the special cases h=0 (the axis passes through one end of the rod) and h=L//2 (the axis passes through the middle of the rod). Express your answers in terms of M and L separated by a comma. I_(h=0),I_(h=L//2)= Part I Is the acceleration magnitude from Part G constant? Would you expect it to be? Yes, because the angular acceleration is constant. No, because the tangential component of the acceleration depends on time. No, because the radial component of the acceleration depends on time.
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