Final answer:
The angular displacement during the 25-second time interval is 15.7 radians. The linear speed of a point on the globe's equator is 0.10 m/s. The average torque provided by the motor during the 25-second time interval can't be calculated without the mass of the globe.
Step-by-step explanation:
To find the angular displacement during the 25-second time interval, we need to use the equation μ = Δθ / Δt, where μ is the angular displacement, Δθ is the change in angle, and Δt is the change in time. Using the given values, we have μ = 0.628 rad/s * 25 s = 15.7 radians.
To find the linear speed of a point on the globe's equator, we can use the equation v = Χr, where v is the linear speed, Χ is the angular velocity, and r is the radius. Using the given values, we have v = 0.628 rad/s * 0.16 m = 0.10 m/s.
To find the average torque provided by the motor during the 25-second time interval, we can use the equation Τ = Iα, where Τ is the torque, I is the moment of inertia, and α is the angular acceleration. Since the globe starts from rest, the initial angular velocity is 0, and we can use the equation α = Χ / Δt to find the angular acceleration. Using the given values, we have α = (0.628 rad/s - 0 rad/s) / 25 s = 0.02512 rad/s². The moment of inertia of a solid sphere is I = (2/5) * m * r², where m is the mass and r is the radius. Since the globe is hollow, we can use the parallel-axis theorem to find the moment of inertia. Assuming the globe has uniform density, the moment of inertia is I = (2/3) * m * r². The average torque is then Τ = (2/3) * m * r² * α. Since we do not have the mass of the globe, we cannot calculate the torque.