A 10.0 kg toy car moves along an x axis with a velocity given by v = -7.89t³ i m/s, with t in seconds. For t> 0, what are (a) the angular momentum of the car and (b) the torque Ť on the car, both calculated about the origin? What are (c) L and (d) 7 about the point (5.92 m, 6.76 m, 0)? What are (e) L and (f) 7 about the point (5.92 m, -6.76 m, 0)?

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**Problem Statement:**

A 10.0 kg toy car moves along an x-axis with a velocity given by \( \vec{v} = -7.89t^3 \hat{\imath} \, \text{m/s} \), with \( t \) in seconds. For \( t > 0 \), calculate:

- (a) the angular momentum \( \vec{L} \) of the car about the origin.
- (b) the torque \( \vec{\tau} \) on the car about the origin.

Calculations are also required for:

- (c) \( \vec{L} \) about the point (5.92 m, 6.76 m, 0).
- (d) \( \vec{\tau} \) about the point (5.92 m, 6.76 m, 0).
- (e) \( \vec{L} \) about the point (5.92 m, -6.76 m, 0).
- (f) \( \vec{\tau} \) about the point (5.92 m, -6.76 m, 0).

**Calculation Template:**

For each of the above calculations, fill in the appropriate values into the expressions below:

- \((a)\) \( \left( \_\_\_ \right) \hat{\jmath} + \left( \_\_\_ \right) \hat{k} \)
- \((b)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \)
- \((c)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^3 \)
- \((d)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^2 \)
- \((e)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^3 \)
- \((f)\) \( \left( \_\_\_ \right) \hat
Transcribed Image Text:**Problem Statement:** A 10.0 kg toy car moves along an x-axis with a velocity given by \( \vec{v} = -7.89t^3 \hat{\imath} \, \text{m/s} \), with \( t \) in seconds. For \( t > 0 \), calculate: - (a) the angular momentum \( \vec{L} \) of the car about the origin. - (b) the torque \( \vec{\tau} \) on the car about the origin. Calculations are also required for: - (c) \( \vec{L} \) about the point (5.92 m, 6.76 m, 0). - (d) \( \vec{\tau} \) about the point (5.92 m, 6.76 m, 0). - (e) \( \vec{L} \) about the point (5.92 m, -6.76 m, 0). - (f) \( \vec{\tau} \) about the point (5.92 m, -6.76 m, 0). **Calculation Template:** For each of the above calculations, fill in the appropriate values into the expressions below: - \((a)\) \( \left( \_\_\_ \right) \hat{\jmath} + \left( \_\_\_ \right) \hat{k} \) - \((b)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \) - \((c)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^3 \) - \((d)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^2 \) - \((e)\) \( \left( \_\_\_ \right) \hat{\imath} + \left( \_\_\_ \right) \hat{k} \cdot t^3 \) - \((f)\) \( \left( \_\_\_ \right) \hat
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